Question

Question #d9f0b

Answer 1

`2/(2x+11)-1/(x-4)=1/2`

`(2(x-4) - 1(2x+11))/((2x+11)(x-4) )=1/2`

`(2x-8-2x-11)/(2x^2+11x-8x-44) = 1/2`

`(-19)/(2x^2+3x-44) = 1/2`

`-38=2x^2+3x-44`

`=2x^2+3x+38-44`

`=2x^2+3x-6`

Answer 2

Get rid of the denominators by multiplying through by the LCM.

Move all the terms to one side and simplify.

Explanation:

You need to get rid of the denominators in the given equation.
You can do this by multiplying each term by the LCM of the denominators, which is `color(blue)(2(2x+11)(x-4))`..

Each denominator will cancel.

The left side will look like this:

`(2xxcolor(blue)(2cancel((2x+11))(x-4)))/cancel((2x+11)) -(1xxcolor(blue)(2(2x+11)cancel((x-4))))/cancel((x-4))`

and the right side like this: `(1xxcolor(blue)(cancel2(2x+11)(x-4)))/cancel2`

This leaves the equation without fractions.

`4(x-4) -2(2x+11) = (2x+11)(x-4)`

Multiply out the brackets:

`4x-16 -4x-22 = 2x^2 +3x-44`

Move all the terms to the right hand side.

`0 = 2x^2 +3x -44+38`

`0 = 2x^2 +3x -6`

This is the required equation.