Question P.6.3: Multiplying Rational Expressions Multiply: x - 7/x - 1·x² - ...
Multiplying Rational Expressions
Multiply: \frac{x-7}{x-1} \cdot \frac{x^2-1}{3 x-21}.
\begin{array}{ll}\frac{x-7}{x-1} \cdot \frac{x^2-1}{3 x-21}&\text{This is the given multiplication problem.}\\=\frac{x-7}{x-1} \cdot \frac{(x+1)(x-1)}{3(x-7)}&\text{Factor as many numerators and denominators }\\&\text{as possible. Because the denominators have }\\& \text{factors of x – 1 and x – 7,} x ≠ 1 \text{ and }x ≠ 7.\\=\frac{\overset{1}{\cancel{x-7}}}{\underset{1}{\bcancel{x-1}} } \cdot \frac{(x+1)\overset{1}{\bcancel{(x-1)}} }{3\underset{1}{\cancel{(x-7)}}}&\text{ Divide numerators and denominators by common factors.}\end{array}
Multiply the remaining factors in the numerators and denominators.
Related Answered Questions
Question: P.6.2
Verified Answer:
a. \frac{x^3+x^2}{x+1}=\frac{x^2(x+1)}{x+1}...
Question: P.6.12
Verified Answer:
\frac{\sqrt{9 - x²}+ \frac{x²}{\sqrt{9 - x²...
Question: P.6.11
Verified Answer:
We will use the method of multiplying each of the ...
Question: P.6.9
Verified Answer:
Step 1 Find the least common denominator. Start b...
Question: P.6.8
Verified Answer:
Step 1 Find the least common denominator. In Exa...
Question: P.6.5
Verified Answer:
Subtract numerators and include parent...
Question: P.6.13
Verified Answer:
The conjugate of the numerator is \sqrt{x+h...
Question: P.6.10
Verified Answer:
Step 1 Add to get a single rational expression i...
Question: P.6.6
Verified Answer:
Step 1 Factor each denominator completely.
2x - 3 ...
Question: P.6.4
Verified Answer:
This is the given division problem.
\be...