Question

How do you solve `\frac { 7} { x + 6} + \frac { 5} { x - 6} = \frac { 6} { ( x + 6) ( x - 6) }`?

Answer 1

`x=3/2`

`3` is the numerator and `2` is the denominator.

Explanation:

Let's solve your equation step-by-step.

Multiply all terms to get `(x+6)(x-6)` as the denominators and cancel:

`7(x−6)+5(x+6)=6`

`12x−12=6" "`(Simplify both sides of the equation)

`12x−12+12=6+12" "`(Add `12` to both sides)

`12x=18`

`(12x)/12=18/12" "`(Divide both sides by `12`)

`x=3/2`

Check the answer. (Plug it in to make sure it works)

`x=3/2" "`(Works in original equation)

Answer:

`x=3/2`

(`3` is the numerator and `2` is the denominator)

Answer 2

`x=3/2`

Explanation:

First, rule out the solutions `x=6` and `x=-6` since they will result in indeterminate forms (dividing by 0).

Now, multiply both sides by `(x+6)(x-6)`

`7(x-6)+5(x+6)=6 " "x !in{-6,6}`

From here, distribute and solve normally, keeping in mind the extraneous solutions -6 and 6.

`7x-42+5x+30=6 color(white)"XXXXX" x!in{-6,6}`
`color(white)"XXX/XX"12x-12=6 color(white)"XXXXX"x!in{-6,6}`
`color(white)"XXXXXXXX.." 12x=18 color(white)"XXXX."x!in{-6,6}`
`color(white)"XXXXXXXXXX" x=3/2`

Final Answer