# How do you solve \frac { t + 4} { t + 6} = \frac { t + 3} { t + 7}?

Jun 27, 2017

You cross-multiply: $\frac{A}{B} = \frac{C}{D} \to A \times D = B \times C$

#### Explanation:

$\left(t + 4\right) \left(t + 7\right) = \left(t + 6\right) \left(t + 3\right) \to$

FOIL:

${t}^{2} + 7 t + 4 t + 28 = {t}^{2} + 6 t + 3 t + 18 \to$

Bring all $t$'s to one side, the numbers to the other
(note that the ${t}^{2}$'s cancel out):

$7 t + 4 t - 6 t - 3 t = 18 - 28 \to 2 t = - 10 \to t = - 5$

Check into the original equation:

$\frac{- 5 + 4}{- 5 + 6} = \frac{- 5 + 3}{- 5 + 7} \to \frac{- 1}{1} = \frac{- 2}{2}$ Check!