Question

question #4 divide the rational expressions. write the quotient in simplest form. $\frac{7b}{10b^{2}}div\frac{4}{3}$ $\frac{40}{21b}$ $\frac{14}{15b}$ $\frac{7}{10b}$ $\frac{21}{40b}$ question #5 the product of two rational expressions requires you to multiply the first rational expression by the reciprocal of the second rational expression. false true

Explanation:

Step1: Change division to multiplication

To divide by a fraction, multiply by its reciprocal. So $\frac{7b}{10b^{2}}\div\frac{4}{3}=\frac{7b}{10b^{2}}\times\frac{3}{4}$.

Step2: Multiply numerators and denominators

Multiply the numerators $7b\times3 = 21b$ and the denominators $10b^{2}\times4=40b^{2}$. The result is $\frac{21b}{40b^{2}}$.

Step3: Simplify the rational - expression

Cancel out the common factor $b$ in the numerator and denominator. $\frac{21b}{40b^{2}}=\frac{21}{40b}$.

Step4: Answer for Question #5

The statement "The product of two rational expressions requires you to multiply the first rational expression by the reciprocal of the second rational expression" is false. To find the product of two rational expressions, you simply multiply the numerators together and the denominators together. For example, if you have $\frac{a}{b}$ and $\frac{c}{d}$, their product is $\frac{a\times c}{b\times d}=\frac{ac}{bd}$. To find the quotient of two rational expressions, you multiply the first by the reciprocal of the second.

Answer:

Question #4: D. $\frac{21}{40b}$
Question #5: A. False