Question

How do you solve `\frac { q - 3} { q + 1} = \frac { q } { q + 6}`?

Answer 1

`q=9`

Explanation:

You can cross multiply the two fractions.

Let's say we have `a/b` and `c/d`, as the image suggests.

Multiply `a` and `d` to get `(q-3)*(q+6)`. Foil the two binomials to get `q^2+6q-3q-18`, which can be combined to equal `q^2+3q-18`.

Multiply `b` and `c`, `(q+1)` and `q`, to get `q^2+q`.

We can make the two equal to each other.

`q^2+3q-18` now equals `q^2+q`.

We now bring all the variables onto one side of the equation.

Subtract `q^2` from the right side over to the left, so the two cancel out. We now have `3q-18 = q`.

Subtract the `q` from the right side over to the left. As `3q - q = 2q`, we now have `2q-18=0`

Subtract the 18 over to the left side, so now we have `2q=18`.

Divide by two on both sides, to get the variable to its base form.

You should get `q=9`.