Question B.5.5: Writing equivalent rational expressions Convert the first ra...
Writing equivalent rational expressions
Convert the first rational expression into an equivalent one that has the indicated denominator.
a. \frac{3}{2 a}, \frac{?}{6 a b} b. \frac{x-1}{x+2}, \frac{?}{x^{2}+6 x+8} c. \frac{a}{3 b-a}, \frac{?}{a^{2}-9 b^{2}}
a. Compare the two denominators. Since 6ab = 2a(3b), we multiply the numerator and denominator of the first expression by 3b:
\frac{3}{2 a}=\frac{3 \cdot 3 b}{2 a \cdot 3 b}=\frac{9 b}{6 a b}b. Factor the second denominator and compare it to the first. Since x^{2}+6 x+8=(x+2)(x+4) , we multiply the numerator and denominator by x + 4:
\frac{x-1}{x+2}=\frac{(x-1)(x+4)}{(x+2)(x+4)}=\frac{x^{2}+3 x-4}{x^{2}+6 x+8}c. Factor the second denominator as
a^{2}-9 b^{2}=(a-3 b)(a+3 b)=-1(3 b-a)(a+3 b)Since 3b – a is a factor of a^{2}-9 b^{2} , we multiply the numerator and denominator by -1(a + 3b):
\frac{a}{3 b-a}=\frac{a(-1)(a+3 b)}{(3 b-a)(-1)(a+3 b)}=\frac{-a^{2}-3 a b}{a^{2}-9 b^{2}}Related Answered Questions
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