Question:
Find the value of: \( \frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)
Find the value of: \( \frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)
Updated On: Nov 17, 2025
- (x2 - 9)
- (x – 3)
- (x + 5)
- (2x + 3)
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The Correct Option is B
Solution and Explanation
The correct option is (B): (x – 3).
\(\frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)
\(\frac{(x^2-9)(x^2+9)}{(x+5)(2x+3)}\times\frac{2x+3}{(x+3)(x^2+9-3x)}\times\frac{[x^2+9-6x+3x](x+5)}{x^2+9+6x-6x}{}\)
\(\frac{(x-3)(x+3)(x^2+9)}{1}\times\frac{1}{(x+3)(x^2+9-3x)}\times\frac{(x^2+9-3x)}{(x^2+9)}\)
=(x-3).
\(\frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)
\(\frac{(x^2-9)(x^2+9)}{(x+5)(2x+3)}\times\frac{2x+3}{(x+3)(x^2+9-3x)}\times\frac{[x^2+9-6x+3x](x+5)}{x^2+9+6x-6x}{}\)
\(\frac{(x-3)(x+3)(x^2+9)}{1}\times\frac{1}{(x+3)(x^2+9-3x)}\times\frac{(x^2+9-3x)}{(x^2+9)}\)
=(x-3).
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