Question

How do you solve `( x+12 )/( x-4 ) = ( x-3 )/( x-7 )`?

Answer 1

`x=8`

Explanation:

First, we'll cross multiply: if `a/b=c/d` then `a*d=b*c`

`(x+12)(x-7) = (x-4)(x-3)`

Expand

`x^2+5x-84=x^2-7x+12`

Add 84 to both sides and simplify

`x^2+5x cancel(-84 + 84) = x^2-7x+12+84`
`x^2+5x=x^2-7x+96`

Subtract `x^2-7x` from both sides and simplify

`x^2+5x-(x^2-7x)=x^2-7x+96-(x^2-7x)`
`12x=96`

Divide both sides by 12 and simplify

`(cancel(12)x)/cancel(12)=96/12`
`x=8`

~ Alex

Answer 2

`x = 8`

Explanation:

To solve this, we use cross multiplication:

Based on this, in this case you would do:
`(x+12)(x-7) = (x-3)(x-4)`

And now we just expand and simplify:
`x^2 + 12x - 7x - 84 = x^2 - 3x - 4x + 12`

Combine like terms:
`x^2 + 5x - 84 = x^2 - 7x + 12`

Subtract `x^2` on both sides of the equation:
`x^2 color(red)(-x^2) + 5x - 84 = x^2 color(red)(-x^2) - 7x + 12`

`5x - 84 = -7x + 12`

Add `7x` to both sides of the equation:
`5x color(red)(+ 7x) - 84 = -7x color(red)(+7x) + 12`

`12x - 84 = 12`

Add `84` to both sides of the equation:
`12x - 84 color(red)(+ 84) = 12 color(red)(+ 84)`

`12x = 96`

Divide both sides by `12`:
`x = 8`

Hope this helps!