Question

What are all values of `x: \frac { 2} { x + 6} + \frac { 2x } { x + 4} = \frac { 3x } { x + 6}`?

Answer 1

`color(blue)(x=4)color(white)("XX")orcolor(white)("XX")color(blue)(x=-2)`

Explanation:

Given
`color(white)("XXX")2/(x+6)+(2x)/(x+4)=(3x)/(x+6)`

`rArr color(white)("XX")(2x)/(x+4)=(3x-2)/(x+6)`

cross-multiplying:
`color(white)("XXX")(2x) xx (x+6)=(3x-2) xx (x+4)`

`rArrcolor(white)("XX")2x^2+12x=3x^2+10x-8`

`rArrcolor(white)("XX")x^2-2x-8=0`

`rArrcolor(white)("XX")(x-4)(x+2)=0`

#rArr{:(x-4=0,color(white)("XX")orcolor(white)("XX"),x+2=0), (rarrx=4,,rarrx=-2) :}#