How do you solve the rational equation $5 / (x+4) = 4 + 3/ (x-2)$ ?

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Answer 1 · 2018-06-09T07:29:05

$x=1$ or x=-5/2#

Multiplying the whole equation by $(x-2)(x+4)ne 0$
we get
$5(x-2)=4(x-2)(x+4)+3(x+4)$
expanding
$5x-10=4x^2+8x-32+3x+12$

$0=4x^2+6x-10$

$0=x^2+3/2x-5/2$

$x_(1,2)=-3/4pmsqrt(9/16+40/16)$
so
$x=1$
or

$x=5/2$

How do you solve the rational equation 5 / (x+4) = 4 + 3/ (x-2)5 / (x+4) = 4 + 3/ (x-2)?