Standardizing Patient Efficiency Calculations

Technical Documentation for Rational Expression LCD Extraction

Arrange the steps to add and simplify the rational expressions: $\frac{2a}{2ab+b^2} + \frac{3a}{4a^2-b^2}$

Match each polynomial to its completely factored form.

Factor out the greatest common factor, $b$, from the expression $2ab + b^2$. The factored form is $b($_____$)$.

What is the new numerator of $\frac{2a}{2ab+b^2}$ after rewriting it with the least common denominator $b(2a+b)(2a-b)$?

Which two factoring techniques are needed to factor the denominators in $\frac{2a}{2ab + b^2} + \frac{3a}{4a^2 - b^2}$?

Factor $4a^2+ab$.

To rewrite $\frac{2a}{2ab+b^2}$ using the LCD $b(2a+b)(2a-b)$, multiply its numerator and denominator by $(2a-b)$.