Question

How do you solve `\frac { x - 3} { 7x + 5} = \frac { 2} { x + 2}`?

Answer 1

Use cross multiplication.

Explanation:

Cross multiplication states that if `a/b=c/d`, then `a*c=b*d`. Using that, let's solve for `x`!

`(x-3)(x+2)=(7x+5)2`
`x^2-x-6=14x+10`
`x^2-15x-16=0`

Looks we'll have to use the quadratic formula for this one.

`x=(15+-sqrt(15^2-4(1)(-16)))/2`
`x=(15+-sqrt(225+72))/2`
`x=(15+-sqrt(297))/2`
`x=(15+-3sqrt(33))/2`

We have reached our answer.