Question

How do you solve `(3x)/(x-6)=5+18/(x-6)`?

Answer 1

`x=6`

Explanation:

First make the five into a fraction and then add the two fractions together.

`(3x)/(x-6) = (5(x-6))/(x-6) + 18/(x-6)`

`(3x)/(x-6) = (5(x-6) +18)/(x-6)`

`(3x)/(x-6) = (5x -30 +18)/(x-6)`

`(3x)/(x-6) = (5x-12)/(x-6)`

Cross multiply to make a linear equation.

`3x(x-6) = (5x-12)(x-6)`

Cancel out the `(x-6)` on both sides and then simplify to solve for `x`.

`3x = 5x-12 -> 5x-3x =12`

`2x = 12`

`x=6`

Answer 2

`x=6`

Explanation:

Solve:

`(3x)/(x-6)=5+(18)/(x-6)`

Multiply both sides by the least common denominator `(x-6)`.

`color(red)cancel(color(black)((x-6)))xx(3x)/color(red)cancel(color(black)((x-6)))=5(x-6)+18/color(red)cancel(color(black)((x-6)))xxcolor(red)cancel(color(black)((x-6)))`

Simplify.

`3x=5(x-6)+18`

Expand.

`3x=5x-30+18`

Simplify.

`3x=5x-12`

Subtract `5x` from both sides.

`3x-5x=-12`

Simplify.

`-2x=-12`

Divide both sides by `-2`.

`(color(red)cancel(color(black)(-2))^1x)/(color(red)cancel(color(black)(-2)))^1=(color(red)cancel(color(black)(-12)))^(6)/color(red)cancel(color(black)((-2)))^1` `larr` Two negatives make a positive.

Simplify.

`x=6`