I need help solve the equation by fractions


8/(21-y) = 12/(y+19)

I think the answer is y = 5, i just need to know how to do work out. i done some solution like this

first multiply by(21-y)(y+19)(assuming that y = 21 and y = 19:

(21-y)(y+19)8/(21-y) = (21-y)(y+19)12/(y+19)

then cancel and multiply out the brackets:

8(y+19) = 12(21-y)

that is

8x+152 = 12x-96

finally,rearrange the equation as

160x = 104

y=5 is correct.

To multiply by (21-y)(y+19), y must not equal 21 nor -19.

Correct until
8(y+19) = 12(21-y)
Expand:
8y+152=-12y+252
20y=100
y=5

To solve the equation 8/(21-y) = 12/(y+19) by fractions, you have made a mistake in your calculations. Let's go through the correct steps together:

Step 1: Cross multiply the fractions.

This means multiplying the numerator of the first fraction with the denominator of the second fraction, and vice versa:

8(y + 19) = 12(21 - y)

Step 2: Distribute the terms on both sides of the equation:

8y + 152 = 252 - 12y

Step 3: Combine like terms on both sides:

8y + 12y = 252 - 152

20y = 100

Step 4: Divide by 20 to solve for y:

y = 100/20

Simplifying the expression gives you:

y = 5

So, the correct solution for the equation is y = 5.