About Multiplying and Dividing Rational Expressions:
When we multiply or divide rational expressions, we follow the same procedures as we used with fractions. To multiply rational expressions, we factor each and cancel what we can. Afterwards, we find the product of the numerators and place the result over the product of the denominators. To divide rational expressions, we multiply the first rational expression by the reciprocal of the second.
Test Objectives
- Demonstrate the ability to multiply rational expressions
- Demonstrate the ability to divide rational expressions
- Demonstrate the ability to simplify a rational expression
#1:
Instructions: Simplify each.
$$a)\hspace{.2em}\frac{18}{11}\cdot \frac{6}{17x}$$
$$b)\hspace{.2em}\frac{11}{7x}\cdot \frac{20}{6}$$
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#2:
Instructions: Simplify each.
$$a)\hspace{.2em}\frac{x^2 + 14x + 49}{x + 7}\div \frac{x + 7}{x + 2}$$
$$b)\hspace{.2em}\frac{1}{x^2 + 12x + 35}\div \frac{x - 6}{2x^3 + 10x^2}$$
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#3:
Instructions: Simplify each.
$$a)\hspace{.2em}\frac{1}{8x - 48}\cdot \frac{x^2 - 12x + 36}{x - 8}$$
$$b)\hspace{.2em}\frac{2x - 8}{10x^2 + 2x}\div \frac{2x^2 + 4x - 48}{45x^2 + 9x}$$
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#4:
Instructions: Simplify each.
$$a)\hspace{.2em}\frac{5x - 3}{5x^2 + 32x - 21}\div \frac{35x^3 - 5x^2}{28x - 4}$$
$$b)\hspace{.2em}\frac{7x^2 + 47x - 14}{14x^2 - 63x}\div \frac{42x^3 - 12x^2}{14x^2 - 63x}$$
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#5:
Instructions: Simplify each.
$$a)\hspace{.2em}\frac{8x - 36}{2x^2 + 9x + 9}\cdot \frac{6x + 9}{6x - 27}$$
$$b)\hspace{.2em}\frac{14x^3 - 42x^2}{6x - 18}\cdot \frac{9x + 24}{24x^3 + 64x^2}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}\frac{108}{187x}$$
$$b)\hspace{.2em}\frac{110}{21x}$$
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#2:
Solutions:
$$a)\hspace{.2em}x + 2$$
$$b)\hspace{.2em}\frac{2x^2}{(x + 7)(x - 6)}$$
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#3:
Solutions:
$$a)\hspace{.2em}\frac{x - 6}{8(x - 8)}$$
$$b)\hspace{.2em}\frac{9}{2(x + 6)}$$
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#4:
Solutions:
$$a)\hspace{.2em}\frac{4}{5x^2(x + 7)}$$
$$b)\hspace{.2em}\frac{x + 7}{6x^2}$$
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#5:
Solutions:
$$a)\hspace{.2em}\frac{4}{x + 3}$$
$$b)\hspace{.2em}\frac{7}{8}$$
