Question

How do you solve the rational equation `(4-8x)/(1-x+4)=8/(x+1)`?

Answer 1

`[4-8x]/[1-x+4]=8/[x+1]`

`[4-8x]/[5-x]=8/[x+1]`

Cross multiply to remove the fractions

`(4-8x)(x+1)=8(5-x)`

Expand the brackets

`4x+4-8x^2-8x=40-8x`

`4-4x-8x^2=40-8x`

Add `8x^2` to both sides

`4-4x=8x^2-8x+40`

add `4x` to both sides

4=8x^2-4x+40#

subtract 4 from both sides

`8x^2-4x+36=0`

Divide both sides by 4

`2x^2-x+9=0`

Put into the quadratic formula

`x=[1\pmsqrt[1-4xx2xx9]]/[2xx2]`

`x=[1\pmsqrt[-71]]/4`

No solutions as you have a negative number in the square root sign