Which of the following is equivalent to (((2x-6)/(y)))/(((x-3)/(y+1))) ? Choose 1 answer: (A) 2 (B) (2x-6)/(x-3) (C) (y+1)/(2y) (D) (2(y+1))/(y)

Simplify Expression: First, let's simplify the given expression by recognizing that dividing by a fraction is equivalent to multiplying by its reciprocal. The given expression is: \[ \frac{\frac{2x-6}{y}}{\frac{x-3}{y+1}} \] To divide by a fraction, we multiply by its reciprocal. So, we rewrite the expression as: \[ \frac{2x-6}{y} \times \frac{y+1}{x-3} \]Factorize Numerator: Next, we notice that $2x-6$ can be factored as $2(x-3)$. This simplification will help us see if there's any cancellation possible. So, the expression becomes: \[ \frac{2(x-3)}{y} \times \frac{y+1}{x-3} \]Cancel Terms: Now, we look for terms that can cancel out. We see that the $(x-3)$ terms in the numerator and denominator can cancel out, leaving us with: \[ \frac{2}{y} \times \frac{y+1}{1} \] This simplifies to: \[ \frac{2(y+1)}{y} \]Compare with Options: Finally, we compare the simplified expression to the given options. The expression $\frac{2(y+1)}{y}$ matches option (D). Therefore, the equivalent expression is: \[ \frac{2(y+1)}{y} \]

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Which of the following is equivalent to
(((2x-6)/(y)))/(((x-3)/(y+1))) ?
Choose 1 answer:
(A) 2
(B)
(2x-6)/(x-3)
(C)
(y+1)/(2y)
(D)
(2(y+1))/(y)

Which of the following is equivalent to $\frac{\left(\frac{2 x-6}{y}\right)}{\left(\frac{x-3}{y+1}\right)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2$ $\newline$ (B) $\frac{2 x-6}{x-3}$ $\newline$ (C) $\frac{y+1}{2 y}$ $\newline$ (D) $\frac{2(y+1)}{y}$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to

\frac{\left(\frac{2 x-6}{y}\right)}{\left(\frac{x-3}{y+1}\right)}

\newline

Choose

1

answer:

\newline

(A)

2

\newline

(B)

\frac{2 x-6}{x-3}

\newline

(C)

\frac{y+1}{2 y}

\newline

(D)

\frac{2(y+1)}{y}

Simplify Expression: First, let's simplify the given expression by recognizing that dividing by a fraction is equivalent to multiplying by its reciprocal. The given expression is: $\newline$ $\frac{\frac{2x-6}{y}}{\frac{x-3}{y+1}}$ $\newline$ To divide by a fraction, we multiply by its reciprocal. So, we rewrite the expression as: $\newline$ $\frac{2x-6}{y} \times \frac{y+1}{x-3}$
Factorize Numerator: Next, we notice that $2x-6$ can be factored as $2(x-3)$ . This simplification will help us see if there's any cancellation possible. So, the expression becomes: $\newline$ $\frac{2(x-3)}{y} \times \frac{y+1}{x-3}$
Cancel Terms: Now, we look for terms that can cancel out. We see that the $(x-3)$ terms in the numerator and denominator can cancel out, leaving us with: $\newline$ $\frac{2}{y} \times \frac{y+1}{1}$ $\newline$ This simplifies to: $\newline$ $\frac{2(y+1)}{y}$
Compare with Options: Finally, we compare the simplified expression to the given options. The expression $\frac{2(y+1)}{y}$ matches option (D). Therefore, the equivalent expression is: $\newline$ $\frac{2(y+1)}{y}$