Multiplying rational expressions - Rational Equations and Expressions

Multiplying rational expressions

Lessons

Notes:

$\bullet$ multiplication rule: $x^a \cdot x^b=x^{a+b}$
$\bullet$ division rule: $\frac{x^a}{x^b}=x^{a-b}$

3.
Convert Expressions to Factored Form, then multiply
State the non-permissible values, then simplify:

Multiplying rational expressions

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Get Started Now

Let's keep going.

Play next lesson

Let's learn the next topic

Let's keep going.

Play next lesson

Let's learn the next topic

Goto next topic

Let's keep going

Let's keep going!

Play next lesson or Practice this topic

Start now and get better math marks!

Keep exploring StudyPug

Start now and get better math marks!

Keep exploring StudyPug

Intro Lesson:

Selected

Lesson: 1

Lesson: 2

Lesson: 3a

Lesson: 3b

Lesson: 3c

Intro

Learn

Practice

Do better in math today

Don't just watch, practice makes perfect.

Do better in math today

Don't just watch, practice makes perfect.

Lessons

Notes:

∙ \bullet ∙ multiplication rule: xa⋅xb=xa+bx^a \cdot x^b=x^{a+b}x​a​​⋅x​b​​=x​a+b​​ ∙ \bullet∙ division rule: xaxb=xa−b\frac{x^a}{x^b}=x^{a-b}​x​b​​​​x​a​​​​=x​a−b​​

Intro Lesson

Review: Multiplying Monomials

1.

2.

Multiplying Rational Expressions in Factored Form State the non-permissible values, then simplify: (x+2)(x−12)(x+4)×2(x+4)x(x+2)\frac{(x+2)}{(x-12)(x+4)} \times \frac{2(x+4)}{x(x+2)}​(x−12)(x+4)​​(x+2)​​×​x(x+2)​​2(x+4)​​

3.

Convert Expressions to Factored Form, then multiply State the non-permissible values, then simplify:

a)

5x2−15x30x2−10x×3x2+8x−3(x2−9) \frac{5x^2-15x}{30x^2-10x} \times \frac{3x^2+8x-3}{(x^2-9)} ​30x​2​​−10x​​5x​2​​−15x​​×​(x​2​​−9)​​3x​2​​+8x−3​​

b)

5x+208x−4×10x−5(4+x)2 \frac{5x+20}{8x-4} \times \frac{10x-5}{(4+x)^2} ​8x−4​​5x+20​​×​(4+x)​2​​​​10x−5​​

c)

(x2+9x+8)(49x3−x)(7x2+55x−8)(x2+x) \frac{(x^2+9x+8)(49x^3-x)}{(7x^2+55x-8)(x^2+x)} ​(7x​2​​+55x−8)(x​2​​+x)​​(x​2​​+9x+8)(49x​3​​−x)​​

Multiplying rational expressions

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

or

$\bullet$ multiplication rule: $x^a \cdot x^b=x^{a+b}$
$\bullet$ division rule: $\frac{x^a}{x^b}=x^{a-b}$

Multiplying Rational Expressions in Factored Form
State the non-permissible values, then simplify:
$\frac{(x+2)}{(x-12)(x+4)} \times \frac{2(x+4)}{x(x+2)}$

Convert Expressions to Factored Form, then multiply
State the non-permissible values, then simplify:

$\frac{5x^2-15x}{30x^2-10x} \times \frac{3x^2+8x-3}{(x^2-9)}$

$\frac{5x+20}{8x-4} \times \frac{10x-5}{(4+x)^2}$

$\frac{(x^2+9x+8)(49x^3-x)}{(7x^2+55x-8)(x^2+x)}$