For y!=0, which of the following expressions is equivalent to (36y^(2)+36 y)/(-32y^(2)-16 y)" ? " Choose 1 answer: (A) (9y+9)/(-8y+4) (B) (9y+9)/(8y+4) (C) (y+1)/(-8y-4) (D) (9y+9)/(-8y-4)

Factor out common terms: Factor out the common terms in the numerator and the denominator. The numerator 36y^2 + 36y can be factored out as 36y(y + 1). The denominator -32y^2 - 16y can be factored out as -16y(2y + 1).Cancel out y term: Simplify the expression by canceling out the common y term from the numerator and the denominator. The y term in the numerator and the denominator can be canceled out because y is not equal to 0 (as given in the problem statement). This gives us (36(y + 1))/(-16(2y + 1)).Simplify constants: Simplify the constants in the expression. We can divide both 36 and -16 by their greatest common divisor, which is 4. This simplifies the expression to (9(y + 1))/(-4(2y + 1)).Distribute negative sign: Distribute the negative sign in the denominator. We can write -4(2y + 1) as (-8y - 4). Now the expression is (9(y + 1))/(-8y - 4).Check answer choices: Check the answer choices to find the equivalent expression. The expression (9(y + 1))/(-8y - 4) matches with answer choice (D) (9y+9)/(-8y-4).

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

(36y^(2)+36 y)/(-32y^(2)-16 y)" ? "
Choose 1 answer:
(A)
(9y+9)/(-8y+4)
(B)
(9y+9)/(8y+4)
(C)
(y+1)/(-8y-4)
(D)
(9y+9)/(-8y-4)

For $y \neq 0$ , which of the following expressions is equivalent to $\newline$ $\frac{36 y^{2}+36 y}{-32 y^{2}-16 y} \text { ? }$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{9 y+9}{-8 y+4}$ $\newline$ (B) $\frac{9 y+9}{8 y+4}$ $\newline$ (C) $\frac{y+1}{-8 y-4}$ $\newline$ (D) $\frac{9 y+9}{-8 y-4}$

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Math Problems

Algebra 1

Identify equivalent linear expressions

Full solution

Q. For

y \neq 0

, which of the following expressions is equivalent to

\newline

\frac{36 y^{2}+36 y}{-32 y^{2}-16 y} \text { ? }

\newline

Choose

1

answer:

\newline

(A)

\frac{9 y+9}{-8 y+4}

\newline

(B)

\frac{9 y+9}{8 y+4}

\newline

(C)

\frac{y+1}{-8 y-4}

\newline

(D)

\frac{9 y+9}{-8 y-4}

Factor out common terms: Factor out the common terms in the numerator and the denominator. $\newline$ The numerator $36y^2 + 36y$ can be factored out as $36y(y + 1)$ . $\newline$ The denominator $-32y^2 - 16y$ can be factored out as $-16y(2y + 1)$ .
Cancel out y term: Simplify the expression by canceling out the common y term from the numerator and the denominator. $\newline$ The y term in the numerator and the denominator can be canceled out because $y \neq 0$ (as given in the problem statement). $\newline$ This gives us $\frac{36(y + 1)}{-16(2y + 1)}$ .
Simplify constants: Simplify the constants in the expression. $\newline$ We can divide both $36$ and $-16$ by their greatest common divisor, which is $4$ . $\newline$ This simplifies the expression to $\left(\frac{9(y + 1)}{-4(2y + 1)}\right)$ .
Distribute negative sign: Distribute the negative sign in the denominator. $\newline$ We can write $-4(2y + 1)$ as $(-8y - 4)$ . $\newline$ Now the expression is $\frac{9(y + 1)}{-8y - 4}$ .
Check answer choices: Check the answer choices to find the equivalent expression. $\newline$ The expression $(9(y + 1))/(-8y - 4)$ matches with answer choice (D) $(9y+9)/(-8y-4)$ .