Question

4/x+3/x+2=2x+2/x^2+2x+7/2x+4? Find value of x Thanks

Answer 1

`x=-4/11`

Explanation:

Given:

`4/x+3/(x+2)=(2x+2)/(x^2+2x)+7/(2x+4)`

Taking LCM

`(4(x+2)+3x)/(x(x+2))=((2x+2)(2x+4)+7(x^2+2x))/((x^2+2x)(2x+4))`

Simplifying
`(4(x+2)+3x)/(x(x+2))=((2x+2)(2x+4)+7(x^2+2x))/(x(x+2)2(x+2)`

Cancelling the common terms in the denominator

`(4(x+2)+3x)=((2x+2)(2x+4)+7(x^2+2x))/(2(x+2)`

Further simplifying

`4(x+2)+3x=(2(x+1)2(x+2)+7x(x+2))/(2(x+2))`

Taking x+2 common in rhs

`4(x+2)+3x=((x+2)(2(x+1)2+7x))/(2(x+2))`

Cancelling x+2 in rhs

`4(x+2)+3x=(2(x+1)2+7x)/2`

`8x+8+3x=1/2xx(4x+4+7x)`

`11x+8=1/2xx(11x+4)`

`11x+4=11/2x+2`

`11x-11/2x=2-4`

`11x/2=-2`

`x=-4/11`