Simplify the expression ?

Question

Simplify the expression

f(x) =

5 +( 10 / x-3)

/

4 + 32 ( x / x^2 − 9)

as much as possible.

Answer 1

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Answer 2

Let's first simplify the numerator

5(x-3)+10/(x-3)

5x-15+10/(X-3)

5x-5/(x-3)

5(x-1)/(x-3)

Let's go 2 the denominator

4(x^2-9)+32x/x^2-9...............(note that x^2-9=(x+3)(x-3)

4x^2-36+32x/(x+3)(x-3)

factorizing....

4(x^2+8x-9)/(x+3)(x-3)

factorizing again....

4(x+9)(X-1)/(x-3)(x+3)

NOW both the num. and the denom.

5(x-1)/(x-3)

..................

4(x+9)(X-1)/(x-3)(x+3)

cancelling (x-3) and (x-1)...

5(1)/[(x+3)/4(x+9)]

5(x+3)/4(x+9)

So the final answer is....

5(x+3)/4(x+9)