How do you simplify (25-x^2)/12 *(6x^2)/(5-x)?

1 Answer
Sheffy
Apr 27, 2016

=(x^2(5+x))/2

Explanation:

(25-x^2)/12xx(6x^2)/(5-x)

Here, 25-x^2 can be written as 5^2-x^2 .

This is of the form a^2-b^2

And we know that a^2-b^2=(a-b)(a+b)

Therefore, we have 5^2-x^2=(5-x)(5+x)

Back to the given expression:

(25-x^2)/12xx(6x^2)/(5-x)

= ((5-x)(5+x))/12xx(6x^2)/(5-x)

(5-x) is common to the numerator and the denominator, and is cancelled out.

=(5+x)/12xx6x^2

Next, we know that 2xx 6 = 12.

=(5+x)/(2xx6)xx6x^2

Cancel 6 from the numerator and denominator.

=(5+x)/2xxx^2

=(x^2(5+x))/2

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