Question
Perform the indicated operations and, if possible, simplify.$$\frac{2 x+4 y}{2 x^{2}+5 x y+2 y^{2}} \cdot \frac{4 x^{2}-y^{2}}{8 x^{2}-8} \div \frac{x^{2}+4 x y+4 y^{2}}{x^{2}-6 x y+9 y^{2}}$$
Step 1
The given expression is $$ \frac{2 x+4 y}{2 x^{2}+5 x y+2 y^{2}} \cdot \frac{4 x^{2}-y^{2}}{8 x^{2}-8} \div \frac{x^{2}+4 x y+4 y^{2}}{x^{2}-6 x y+9 y^{2}} $$ We can factorize the expressions as follows: $$ \frac{2(x+2y)}{2(x+y)^2} \cdot Show more…
Show all steps
Your feedback will help us improve your experience
Ankit Gupta and 99 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Perform the operations. Simplify, if possible $\frac{x^{2}-y^{2}}{2 x^{4}-2 x^{3}} \div\left(\frac{x-y}{2 x^{2}} \div \frac{x+y}{x^{2}+2 x y+y^{2}}\right)$
Rational Expressions and Equations
Multiplying and Dividing Rational Expressions
Perform the indicated operations and, if possible, simplify. $$ \frac{4 x^{2}-9 y^{2}}{8 x^{3}-27 y^{3}} \div \frac{4 x+6 y}{3 x-9 y} \cdot \frac{4 x^{2}+6 x y+9 y^{2}}{4 x^{2}-8 x y+3 y^{2}} $$
Rational Expressions, Equations, and Functions
Rational Expressions and Functions: Multiplying and Dividing
Perform the indicated operations and simplify as completely as possible. $$\frac{x^{3} y-x y^{3}}{8 x^{2} y+4 x y^{2}} \div \frac{(x-y)^{2}}{2 x^{2}+3 x y+y^{2}}$$
More Rational Expressions
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD