Question

Simplify a) x^2+3x+2/x^2-3x-10 and b) x^2+x-2/4 divided by x-1/2x

Answer 1

a) you can factor x^2+3x+2 into (x+1)(x+2)
and you can factor x^2-3x-10 into (x-5)(x+2)

so the x+2 cancels and youre left with (x+1)/(x-5)

b) you can first flip the second fraction and then multiply them:

so now its: x^2+x-2/4 * 2x/(x-1)

now factor x^2+x-2 into (x+2)(x-1)

(x+2)(x-1)/4 * 2x/(x-1)

the x-1 and the 2 cancel. so youre left with

(x+2)/2 * x

which is x(x+2)/2

Answer 2

a) you can factor x^2+3x+2 into (x+1)(x+2)
and you can factor x^2-3x-10 into (x-5)(x+2)

so the x+2 cancels and youre left with (x+1)/(x-5)

b) you can first flip the second fraction and then multiply them:

so now its: x^2+x-2/4 * 2x/(x-1)

now factor x^2+x-2 into (x+2)(x-1)

(x+2)(x-1)/4 * 2x/(x-1)

the x-1 and the 2 cancel. so youre left with

(x+2)/2 * x

which is x(x+2)/2