Question:
Simplify the expression: \( \frac{3x - 4}{x} + \frac{2x + 5}{x} \).
Options
Simplify the expression: \( \frac{3x - 4}{x} + \frac{2x + 5}{x} \).
Options
Show Hint
When adding algebraic fractions with the same denominator, combine the numerators first, then simplify.
Updated On: Oct 4, 2025
- \( \frac{5x + 1}{x} \)
- \( 5 + \frac{1}{x} \)
- \( \frac{5}{x} + 1 \)
- \( \frac{1}{x} - 5 \)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
We are tasked with simplifying the sum of two fractions. The two fractions have the same denominator, so we can combine them directly.
Step 1: Combine the fractions.
The two fractions are \( \frac{3x - 4}{x} \) and \( \frac{2x + 5}{x} \), which share the same denominator \( x \). To combine them, we add the numerators and keep the common denominator: \[ \frac{3x - 4}{x} + \frac{2x + 5}{x} = \frac{(3x - 4 + 2x + 5)}{x}. \]
[6pt] Step 2: Simplify the numerator.
Now simplify the numerator by combining like terms: \[ 3x + 2x = 5x
\text{and}
-4 + 5 = 1. \] So, the expression becomes: \[ \frac{5x + 1}{x}. \]
[6pt] Step 3: Simplify the expression further.
We can now split the fraction into two parts: \[ \frac{5x + 1}{x} = \frac{5x}{x} + \frac{1}{x}. \] Simplify each term: \[ \frac{5x}{x} = 5
\text{and}
\frac{1}{x} \text{ stays as is}. \] Thus, the expression becomes: \[ 5 + \frac{1}{x}. \]
[6pt] Conclusion:
The simplified expression is: \[ \boxed{5 + \frac{1}{x}}. \] This is the final simplified form of the given expression.
The two fractions are \( \frac{3x - 4}{x} \) and \( \frac{2x + 5}{x} \), which share the same denominator \( x \). To combine them, we add the numerators and keep the common denominator: \[ \frac{3x - 4}{x} + \frac{2x + 5}{x} = \frac{(3x - 4 + 2x + 5)}{x}. \]
[6pt] Step 2: Simplify the numerator.
Now simplify the numerator by combining like terms: \[ 3x + 2x = 5x
\text{and}
-4 + 5 = 1. \] So, the expression becomes: \[ \frac{5x + 1}{x}. \]
[6pt] Step 3: Simplify the expression further.
We can now split the fraction into two parts: \[ \frac{5x + 1}{x} = \frac{5x}{x} + \frac{1}{x}. \] Simplify each term: \[ \frac{5x}{x} = 5
\text{and}
\frac{1}{x} \text{ stays as is}. \] Thus, the expression becomes: \[ 5 + \frac{1}{x}. \]
[6pt] Conclusion:
The simplified expression is: \[ \boxed{5 + \frac{1}{x}}. \] This is the final simplified form of the given expression.
Was this answer helpful?
0
0
Top Questions on Algebra
- If \( a_1, a_2, \dots, a_8 \) are the roots of the equation \( x^8 + x^7 + \dots + x + 1 = 0 \), then the value of \( a_1^{2025} + a_2^{2025} + \dots + a_8^{2025} \) is
- Which of the following numbers is divisible by \( 3^{10} + 2 \)?
- Let \( f(x) = a^2x^2 + 2bx + c \) where, a \( \neq \) 0, b, c are real numbers and x is a real variable then
- If \( 8x^2 - 2kx + k = 0 \) is a quadratic equation in x, such that one of its roots is p times the other, and p, k are positive real numbers, then k equals
- Let P(x) be a quadratic polynomial such that \( \begin{vmatrix} P(0) & P(1) \\ P(0) & P(2) \end{vmatrix} = 0 \). Let P(0) = 2 and P(1) + P(2) + P(3) = 14. Then P(4) equals
View More Questions
Questions Asked in GRE exam
- Should we really care for the greatest actors of the past could we have them before us? Should we find them too different from our accent of thought, of feeling, of speech, in a thousand minute particulars which are of the essence of all three? Dr. Doran's long and interesting records of the triumphs of Garrick, and other less familiar, but in their day hardly less astonishing, players, do not relieve one of the doubt. Garrick himself, as sometimes happens with people who have been the subject of much anecdote and other conversation, here as elsewhere, bears no very distinct figure. One hardly sees the wood for the trees. On the other hand, the account of Betterton, "perhaps the greatest of English actors," is delightfully fresh. That intimate friend of Dryden, Tillatson, Pope, who executed a copy of the actor's portrait by Kneller which is still extant, was worthy of their friendship; his career brings out the best elements in stage life. The stage in these volumes presents itself indeed not merely as a mirror of life, but as an illustration of the utmost intensity of life, in the fortunes and characters of the players. Ups and downs, generosity, dark fates, the most delicate goodness, have nowhere been more prominent than in the private existence of those devoted to the public mimicry of men and women. Contact with the stage, almost throughout its history, presents itself as a kind of touchstone, to bring out the bizarrerie, the theatrical tricks and contrasts, of the actual world.
- GRE - 2025
- Reading Comprehension
- “Reviving the practice of using elements of popular music in classical composition, an approach that had been in hibernation in the United States during the 1960s, composer Philip Glass (born 1937) embraced the ethos of popular music in his compositions. Glass based two symphonies on music by rock musicians David Bowie and Brian Eno, but the symphonies' sound is distinctively his. Popular elements do not appear out of place in Glass's classical music, which from its early days has shared certain harmonies and rhythms with rock music. Yet this use of popular elements has not made Glass a composer of popular music. His music is not a version of popular music packaged to attract classical listeners; it is high art for listeners steeped in rock rather than the classics.
- GRE - 2025
- Reading Comprehension
- Called by some the “island that time forgot,” Madagascar is home to a vast array of unique, exotic creatures. One such animal is the aye-aye. First described by western science in 1782, it was initially categorized as a member of the order Rodentia. Further research then revealed that it was more closely related to the lemur, a member of the primate order. Since the aye-aye is so different from its fellow primates, however, it was given its own family: Daubentoniidae. The aye-aye has been listed as an endangered species and, as a result, the government of Madagascar has designated an island off the northeastern coast of Madagascar as a protected reserve for aye-ayes and other wildlife.
Long before Western science became enthralled with this nocturnal denizen of Madagascar’s jungles, the aye-aye had its own reputation with the local people. The aye aye is perhaps best known for its large, round eyes and long, extremely thin middle finger. These adaptations are quite sensible, allowing the aye-aye to see well at night and retrieve grubs, which are one of its primary food sources, from deep within hollow branches. However, the aye-aye’s striking appearance may end up causing its extinction. The people of Madagascar believe that the aye-aye is a type of spirit animal, and that its appearance is an omen of death. Whenever one is sighted, it is immediately killed. When combined with the loss of large swaths of jungle habitat, this practice may result in the loss of a superb .- GRE - 2025
- Reading Comprehension
- It has been suggested that long-term prisoners, on release from jail, be given a reasonable state pension to reduce the likelihood of their resorting to crime. Most people instinctively reject the suggestion as they feel it would be like rewarding criminal activity. The supporters of the prisoners' pension scheme have criticized those who reject this possibility, by claiming that for the critics...
Which of the following is the most logical completion of the sentence above?- GRE - 2025
- Critical Reasoning
- Jean Valjean, the protagonist in Victor Hugo’s novel Les Misérables, spends the bulk of his lengthy _______ plotting a very clever set of revenge schemes, which he executes upon his escape.
- GRE - 2025
- Vocabulary
View More Questions