# How do you solve (1 - y)/(1 + y) = 2/3?

May 30, 2016

$y = \frac{1}{5}$

#### Explanation:

When we have 2 fractions equal to each other then the way to eliminate the fractions is to $\textcolor{b l u e}{\text{cross-multiply}}$

$\Rightarrow \frac{a}{b} = \frac{c}{\mathrm{dr}} A r r a d = b c$

here we obtain

2(1 + y) = 3(1 - y)

multiply out brackets.

hence : 2 + 2y = 3 - 3y

now collect like terms , y to the left and numbers on right. Remember to change the sign of a term when it is moved from one side to the other.

thus : 2y + 3y = 3 - 2 → 5y = 1

divide both sides by 5

$\Rightarrow \frac{{\cancel{5}}^{1} y}{\cancel{5}} ^ 1 = \frac{1}{5} \Rightarrow y = \frac{1}{5}$