For r!=0, which of the following expressions is equivalent to (-24r^(2)-56 r)/(-48r^(2)+64 r)" ? " Choose 1 answer: (A) (-3r+7)/(-6r+8) (B) (-3r-7r)/(-6r+8r) (C) (3r+7)/(-6r+8) (D) (-3r-7)/(-6r+8)

Identify common factor: Identify the common factor in both the numerator and the denominator. The common factor in the numerator (-24r^2 - 56r) is -8r. The common factor in the denominator (-48r^2 + 64r) is -16r.Factor out common factors: Factor out the common factors from the numerator and the denominator. Numerator: -8r(3r + 7) Denominator: -16r(3r - 4)Simplify expression: Simplify the expression by canceling out the common terms. The common term -8r/-16r simplifies to 1/2. So, the expression becomes (1/2)(3r + 7)/(3r - 4).Multiply by 2: Multiply the numerator and the denominator by 2 to get rid of the fraction. The expression becomes (3r + 7)/(2*(3r - 4)).Distribute in denominator: Distribute the 2 in the denominator. The expression becomes (3r + 7)/(6r - 8).Compare with answer choices: Compare the simplified expression with the answer choices. The simplified expression (3r + 7)/(6r - 8) matches with choice (C).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For
r!=0, which of the following expressions is equivalent to

(-24r^(2)-56 r)/(-48r^(2)+64 r)" ? "
Choose 1 answer:
(A)
(-3r+7)/(-6r+8)
(B)
(-3r-7r)/(-6r+8r)
(C)
(3r+7)/(-6r+8)
(D)
(-3r-7)/(-6r+8)

For $r \neq 0$ , which of the following expressions is equivalent to $\frac{-24 r^{2}-56 r}{-48 r^{2}+64 r}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{-3 r+7}{-6 r+8}$ $\newline$ (B) $\frac{-3 r-7 r}{-6 r+8 r}$ $\newline$ (C) $\frac{3 r+7}{-6 r+8}$ $\newline$ (D) $\frac{-3 r-7}{-6 r+8}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. For

r \neq 0

, which of the following expressions is equivalent to

\frac{-24 r^{2}-56 r}{-48 r^{2}+64 r}

\newline

Choose

1

answer:

\newline

(A)

\frac{-3 r+7}{-6 r+8}

\newline

(B)

\frac{-3 r-7 r}{-6 r+8 r}

\newline

(C)

\frac{3 r+7}{-6 r+8}

\newline

(D)

\frac{-3 r-7}{-6 r+8}

Identify common factor: Identify the common factor in both the numerator and the denominator. $\newline$ The common factor in the numerator $(-24r^2 - 56r)$ is $-8r$ . $\newline$ The common factor in the denominator $(-48r^2 + 64r)$ is $-16r$ .
Factor out common factors: Factor out the common factors from the numerator and the denominator. $\newline$ Numerator: $-8r(3r + 7)$ $\newline$ Denominator: $-16r(3r - 4)$
Simplify expression: Simplify the expression by canceling out the common terms. $\newline$ The common term $-\frac{8r}{-16r}$ simplifies to $\frac{1}{2}$ . $\newline$ So, the expression becomes $\left(\frac{1}{2}\right)\left(\frac{3r + 7}{3r - 4}\right)$ .
Multiply by $2$ : Multiply the numerator and the denominator by $2$ to get rid of the fraction. $\newline$ The expression becomes $\frac{3r + 7}{2\times(3r - 4)}$ .
Distribute in denominator: Distribute the $2$ in the denominator. $\newline$ The expression becomes $\frac{3r + 7}{6r - 8}$ .
Compare with answer choices: Compare the simplified expression with the answer choices. $\newline$ The simplified expression $(3r + 7)/(6r - 8)$ matches with choice (C).