Question

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

Answer 1

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

Explanation:

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`