Solve b/a-b:(a/a-b-a+b/a) | Microsoft Math Solver

Evaluate

Expand

Quiz

Algebra

5 problems similar to:

Similar Problems from Web Search

https://socratic.org/questions/if-a-and-b-are-integers-with-a-b-what-is-the-smallest-possible-positive-value-of

https://www.tiger-algebra.com/drill/a2-b2/ab-ab-b2/ab-a2/

https://www.quora.com/If-frac-a-b-b-c-c-a-a+b-b+c-c+a-frac-1-30-whats-the-value-of-frac-b-a+b-+-frac-c-b+c-+-frac-a-c+a-1

Copied to clipboard

\frac{\frac{b}{a-b}}{\frac{aa}{a\left(a-b\right)}-\frac{\left(a+b\right)\left(a-b\right)}{a\left(a-b\right)}}

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-b and a is a\left(a-b\right). Multiply \frac{a}{a-b} times \frac{a}{a}. Multiply \frac{a+b}{a} times \frac{a-b}{a-b}.

\frac{\frac{b}{a-b}}{\frac{aa-\left(a+b\right)\left(a-b\right)}{a\left(a-b\right)}}

Since \frac{aa}{a\left(a-b\right)} and \frac{\left(a+b\right)\left(a-b\right)}{a\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

\frac{\frac{b}{a-b}}{\frac{a^{2}-a^{2}+ab-ba+b^{2}}{a\left(a-b\right)}}

Do the multiplications in aa-\left(a+b\right)\left(a-b\right).

\frac{\frac{b}{a-b}}{\frac{b^{2}}{a\left(a-b\right)}}

Combine like terms in a^{2}-a^{2}+ab-ba+b^{2}.

\frac{ba\left(a-b\right)}{\left(a-b\right)b^{2}}

Divide \frac{b}{a-b} by \frac{b^{2}}{a\left(a-b\right)} by multiplying \frac{b}{a-b} by the reciprocal of \frac{b^{2}}{a\left(a-b\right)}.

\frac{a}{b}

Cancel out b\left(a-b\right) in both numerator and denominator.