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

Question

Ethan Adkins · Accepted Answer

#y=1/5#

When we have 2 fractions equal to each other then the way to eliminate the fractions is to #color(blue)"cross-multiply"#

#rArra/b=c/drArr ad=bc#

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

#rArr(cancel(5)^1 y)/cancel(5)^1=1/5rArry=1/5#

Eva Abramson · Answer

undefined To solve the equation (1 - y)/(1 + y) = 2/3:

1. Cross multiply to eliminate the denominators: (1 - y) * 3 = (1 + y) * 2.
2. Expand both sides: 3 - 3y = 2 + 2y.
3. Rearrange terms: 3 - 2 = 2y + 3y.
4. Simplify: 1 = 5y.
5. Solve for y: y = 1/5.

Nathan Axel · Answer

undefined To solve the equation $ \frac{1 - y}{1 + y} = \frac{2}{3} $, we can start by cross-multiplying to eliminate the fractions and then solve for the variable $ y $. Here's the step-by-step process:

$$ (1 - y) \cdot 3 = (1 + y) \cdot 2 $$

Expand both sides:

$$ 3 - 3y = 2 + 2y $$

Now, combine like terms:

$$ -3y - 2y = 2 - 3 $$

$$ -5y = -1 $$

Finally, solve for $ y $ by dividing both sides by -5:

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

Therefore, the solution to the equation is $ y = \frac{1}{5} $.