# How do you solve the equation and identify any extraneous solutions for 24/5=9/(y+2)?

Jun 11, 2015

Two fractions being equal you use the cross-product:

#### Explanation:

$\mathmr{if} \frac{a}{b} = \frac{c}{d} \to a \cdot d = b \cdot c$

$\to 24 \cdot \left(y + 2\right) = 5 \cdot 9$
$\to 24 y + 48 = 45$
$\to 24 y = - 3$

$y = - \frac{3}{24} = - \frac{1}{8}$

There are no extraneous solutions, as the only "condition" is $y \ne - 2$, as otherwise the numerator of the right fraction $= 0$