Question

Question #a71e9

Answer 1

`x=color(green)(-10/3)`

Explanation:

Given
`color(white)("XXX")4/(x+2)+1/(x+3)=8/(x+2)`

Multiplying both sides by `(x+2)(x+3)`
`color(white)("XXX")4(x+3)+1(x+2)=8(x+3)`

Simplifying
`color(white)("XXX")5x+14=8x+24`

`color(white)("XXX")-3x=10`

`color(white)("XXX")x=-10/3 (=3 1/3)`

Answer 2

`x=-10/3`

Explanation:

Basically we need to isolate `x` so I will first multiply both sides by `x+2`

`4+(x+2)/(x+3)=8`
now move `4` over
`(x+2)/(x+3)=4`
now multiply both sides by `x+3`
`x+2=4x+12`
Move like terms to each side
`-3x=10`
Solve for `x`
`x=-10/3`

As a final step always plug in and check your answer.

Answer 3

`x=-10/3`
This solution is not the most efficient on purpose: The objective is to demonstrates a basic principle that may be used else ware.

Explanation:

Given:`" "4/(x+2)+1/(x+3)=8/(x+2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`[4/(x+2)color(red)(xx1)]+ [1/(x+3)color(blue)(xx1)]" "=" "[8/(x+2)color(green)(xx1)]`

`color(white)(.)`

`[4/(x+2)color(red)(xx(x+3)/(x+3))]+ [1/(x+3)color(blue)(xx(x+2)/(x+2))]=[8/(x+2)color(green)(xx(x+3)/(x+3))]`

`color(white)(.)`

`[(4(x+3))/((x+2)(x+3))] +[(x+2)/((x+2)(x+3))] =[(8(x+3))/((x+2)(x+3))]`
`color(white)(.)`

Multiply both sides by `(x+2)(x+3)` giving:

`4(x+3)" "+" "x+2" "=" "8(x+3)`

`color(white)(.)4x+12" "+" "x+2" "=" "8x+24`

`" "5x+14" "=" "8x+24`

`" "-10" "=" "3x`

`" "x=-10/3`