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Exercises Polynomials and factoring

Example 8.4 from Elementary Algebra, 8.1 Simplify Rational Expressions

Simplify Rational Expressions: example 8.4

Evaluate $\frac{a^{2} + 2 a b + b^{2}}{3 a b^{3}}$ for each value:

ⓐ $a = 1, b = 2$ ⓑ $a = −2, b = −1$ ⓒ $a = \frac{1}{3}, b = 0$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
ⓐ

$\frac{a^{2} + 2 a b + b^{2}}{3 a b^{2}}$ when $a = 1, b = 2$ .

Simplify.

ⓑ

$\frac{a^{2} + 2 a b + b^{2}}{3 a b^{2}}$ when $a = −2, b = −1$ .

Simplify.

ⓒ

$\frac{a^{2} + 2 a b + b^{2}}{3 a b^{2}}$ when $a = −1, b = 2$ .

Simplify.

The expression is undefined.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Evaluate $\frac{2 a^{3} b}{a^{2} + 2 a b + b^{2}}$ for each value:

ⓐ $a = −1, b = 2$ ⓑ $a = 0, b = −1$ ⓒ $a = 1, b = \frac{1}{2}$

How did it go?

PreviousSimplify Rational Expressions: example 8.3 Next Simplify Rational Expressions: example 8.5

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 8.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.