Question

simplify: x+4/2x-8 - x+10/4x-16

Answer 1

\[x + \frac{4x}{2} - 8 - x + \frac{10x}{4} -16 ?\]

Answer 2

Have you had a go, what did you get? :)

Answer 3

Ok I got an answer, I could show you how I did it if that helps you?

Answer 4

I started by cross multiplying (so multiply the left hand side by the bottom of the right and the right hand side by the bottom of the left) and putting it over a common demoninator.

So I got

\[\frac{(x+4)(4x-16) - (x+10)(2x-8)}{(2x-8)(4x-16)}\]

I now multiplied out all the brackets:

\[\frac{ 4x^2 - 64 +16x -16x - (2x^2 - 80 +20x - 8x)}{8x^2 + 128 -32x -32x}\]

I simplified to get

\[\frac{2x^2 +16 -12x}{8x^2 - 64x +128}\]

Divide top and bottom by 2

\[\frac{x^2 + 8 - 6x)}{4x^2 -32x +64}\]

Factorise top and bottom

\[\frac{(x-4)(x-2)}{4(x-4)(x-4)}\]

(x-4) cancels and you are left with

\[\frac{(x-2)}{4(x-4)}\]

Which is your answer :)