Question

Solve the formula for the indicated variable.
T(r+s)=rs, for r
(Simplify your answer.)

Answer 1

Hello!

The distributive property is going to be very important in this. It states that when you have a variable multiplied by a set of parenthesis, you distribute that variable inside the parenthesis (as long as the operations inside the parenthesis are addition or subtraction). For example, 2(x + 4), you can distribute the 2 to x and 4, to get 2x + 2(4).

Now, distribute t to inside the parenthesis.

T(r + s) = rs

Tr + Ts = rs

Now, move everything with an r in it to the right side.

Tr + Ts = rs

Ts = rs - Tr

Use the opposite of the distributive property, to extract r from the right side.

Ts = rs - Tr

Ts = r (s - T)

And divide both sides by s - T to isolate the r.

Ts = r (s - T)

`(Ts)/(s-T)` = r

Hope this helps!

Answer 2

`R = (-TS)/((T-S))`

Explanation:

First, distribute all terms

`T(R+S) =RS\\TR + TS =RS`

Get all terms with R onto the same side

`TR + TS = RS\\TR - RS = -TS`

Factor out the R

`R(T-S)=-TS`

Divide by (T-S) to isolate R

`R = (-TS)/((T-S))`