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

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Answer 1 · 2018-06-04T13:55:10

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

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

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

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