{15(x²-2x-15)}{25(x+3)(x²-25)} is equal to :

Correct Answer is : 35(x+5)3/5(x+5)5(x+5)3

Correct Answer is : 35(x+5)3/5(x+5)5(x+5)3

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CTET Paper II (Mathematics and Science) 13 Jan 2023 Solved Paper

Question : 43 of 150

Marks: +1, -0

\frac{15(x^{2}-2x-15)}{25(x+3)(x^{2}-25)}

is equal to :

Solution:

Concept:

Factorize the numerator and denominator completely, then cancel common factors to simplify the rational expression.

Explanation:

Start with

\frac{15(x^{2}-2x-15)}{25(x+3)(x^{2}-25)}

Factor

x^{2}-2x-15

(x-5)(x+3)

Factor

x^{2}-25

(x+5)(x-5)

So the expression becomes

\frac{15(x-5)(x+3)}{25(x+3)(x+5)(x-5)}

Cancel the common factors

(x+3)

and

(x-5)

Now it is

\frac{15}{25(x+5)}

Simplify

\frac{15}{25}

\frac{3}{5}

Thus the simplified form is

\frac{3}{5(x+5)}

Answer:

The correct option is D.

\frac{3}{5(x+5)}

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