Multiplying rational expressions - Rational Equations and Expressions

Multiplying rational expressions

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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

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Lessons

Notes:

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

Intro Lesson

Review: Multiplying Monomials

1.

Simplifying Rational Expressions Involving Multiplication State the non-permissible values, then simplify: 5x2y3x2y2×9z3x4y215y3z2\frac{5x^2y^3}{x^2y^2} \times \frac{9z^3x^4y^2}{15y^3z^2}x2y25x2y3​×15y3z29z3x4y2​

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)} 30x2−10x5x2−15x​×(x2−9)3x2+8x−3​

b)

5x+208x−4×10x−5(4+x)2 \frac{5x+20}{8x-4} \times \frac{10x-5}{(4+x)^2} 8x−45x+20​×(4+x)210x−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)} (7x2+55x−8)(x2+x)(x2+9x+8)(49x3−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: $\frac{x^a}{x^b}=x^{a-b}$

Simplifying Rational Expressions Involving Multiplication
State the non-permissible values, then simplify:
$\frac{5x^2y^3}{x^2y^2} \times \frac{9z^3x^4y^2}{15y^3z^2}$

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:

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

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

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