#### Answer

$\frac{ta}{a-t}$=b

#### Work Step by Step

$\frac{t}{a}+\frac{t}{b}= 1 ; b$
What this problem is asking for is what does the variable b equal. This is indicated because of the use of the semicolon. The first thing we will do is get rid of the fractions. This will be done by multiplying each number times the LCD of the denominators. In this case, the least common denominator is (ab).
$\frac{t}{a}\times(ab)+\frac{t}{b}\times(ab)=1 \times(ab)$
By multiplying $\frac{t}{a}$ with (ab) the variable a from the fraction will cancel out with the variable a from (ab). You then multiply t $\times$b giving you tb.
tb+ta=ab
Next, we subtract tb from both sides. This is done to get the variable b on one side of the equation.
tb-(tb)+ta=ab-(tb)
ta=ab-tb
We will now factor out b.
ta=b(a-t)
Lastly, you divide (a-t) from both sides.
$\frac{ta}{a-t}=b\frac{a-t}{a-t}$
$\frac{a-t}{a-t}$ will cancel itself out. Your final answer should look like this.
$\frac{ta}{a-t}=b$