(a+b)/(c-d)-(a+b)/(d-c) Which of the following is equivalent to the given expression for c!=d ? Choose 1 answer: (A) 0 (B) (2b)/(c-d) (c) (2(a+b))/(c-d) (D) (2a+2b)/(2c-2d)

Recognize Rule: First, we need to recognize that (d-c) is the same as -(c-d). This means that we can rewrite the second fraction as: (a+b)/(d-c) = (a+b)/(-(c-d)) = -(a+b)/(c-d)Combine Fractions: Now, we can combine the two fractions since they have the same denominator: (a+b)/(c-d) - (a+b)/(c-d) = (a+b)/(c-d) - (-(a+b)/(c-d))Simplify Numerators: Simplify the expression by combining the numerators: (a+b) - (-(a+b)) = (a+b) + (a+b) = 2(a+b)Combine Numerator and Denominator: Now, place the combined numerator over the common denominator: 2(a+b)/(c-d)Check Answer: We can check our answer against the options provided. The expression we have found, 2(a+b)/(c-d), matches option (C).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

(a+b)/(c-d)-(a+b)/(d-c)
Which of the following is equivalent to the given expression for
c!=d ?
Choose 1 answer:
(A) 0
(B)
(2b)/(c-d)
(c)
(2(a+b))/(c-d)
(D)
(2a+2b)/(2c-2d)

$\frac{a+b}{c-d}-\frac{a+b}{d-c}$ $\newline$ Which of the following is equivalent to the given expression for $c \neq d$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $\frac{2 b}{c-d}$ $\newline$ (C) $\frac{2(a+b)}{c-d}$ $\newline$ (D) $\frac{2 a+2 b}{2 c-2 d}$

View step-by-step help

Home

Math Problems

Algebra 1

Identify equivalent linear expressions

Full solution

\frac{a+b}{c-d}-\frac{a+b}{d-c}

\newline

Which of the following is equivalent to the given expression for

c \neq d

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

\frac{2 b}{c-d}

\newline

(C)

\frac{2(a+b)}{c-d}

\newline

(D)

\frac{2 a+2 b}{2 c-2 d}

Recognize Rule: First, we need to recognize that $(d-c)$ is the same as $- (c-d)$ . This means that we can rewrite the second fraction as: $\frac{a+b}{d-c} = \frac{a+b}{-(c-d)} = -\frac{a+b}{c-d}$
Combine Fractions: Now, we can combine the two fractions since they have the same denominator: $(a+b)/(c-d) - (a+b)/(c-d) = (a+b)/(c-d) - (-(a+b)/(c-d))$
Simplify Numerators: Simplify the expression by combining the numerators: $a+b$ - \-$a+b$ = $a+b$ + $a+b$ = ${2}(a+b)$
Combine Numerator and Denominator: Now, place the combined numerator over the common denominator: $\frac{2(a+b)}{c-d}$
Check Answer: We can check our answer against the options provided. The expression we have found, $\frac{2(a+b)}{c-d}$ , matches option (C).