Juan tried to perform the following addition and reduce to lowest terms: (2)/(x-1)+(3)/(x+1) This is his work: {:[=(2)/(x-1)+(3)/(x+1)],[=(2+3)/(x-1+x+1)],[=(5)/(2x)]:} What mistake did he make in combining the rational expressions? (A) He forgot to factor the denominator. (B) He failed to find a common denominator. (C) He incorrectly applied the distributive property. (D) He made a mistake in simplifying the numerators.

Identify Common Denominator: Juan starts with the expression $\frac{2}{x-1} + \frac{3}{x+1}$. He needs to find a common denominator to combine these fractions.Combine Fractions Incorrectly: Juan attempts to combine the fractions by adding the numerators and denominators separately, resulting in $\frac{2+3}{x-1+x+1}$. This is incorrect because he cannot simply add the denominators as if they were like terms. The correct method is to find a common denominator, which would be the product of the two distinct denominators, $(x-1)(x+1)$.

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Juan tried to perform the following addition and reduce to lowest terms: (2)/(x-1)+(3)/(x+1)
This is his work:
{:[=(2)/(x-1)+(3)/(x+1)],[=(2+3)/(x-1+x+1)],[=(5)/(2x)]:}
What mistake did he make in combining the rational expressions?
(A) He forgot to factor the denominator.
(B) He failed to find a common denominator.
(C) He incorrectly applied the distributive property.
(D) He made a mistake in simplifying the numerators.

Juan tried to perform the following addition and reduce to lowest terms: $\frac{2}{x-1}+\frac{3}{x+1}$ $\newline$ This is his work: $\newline$ $\begin{array}{l} =\frac{2}{x-1}+\frac{3}{x+1} \\ =\frac{2+3}{x-1+x+1} \\ =\frac{5}{2 x} \end{array}$ $\newline$ What mistake did he make in combining the rational expressions? $\newline$ (A) He forgot to factor the denominator. $\newline$ (B) He failed to find a common denominator. $\newline$ (C) He incorrectly applied the distributive property. $\newline$ (D) He made a mistake in simplifying the numerators.

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Math Problems

Algebra 1

Write two-variable inequalities: word problems

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Q. Juan tried to perform the following addition and reduce to lowest terms:

\frac{2}{x-1}+\frac{3}{x+1}

\newline

This is his work:

\newline

\begin{array}{l} =\frac{2}{x-1}+\frac{3}{x+1} \\ =\frac{2+3}{x-1+x+1} \\ =\frac{5}{2 x} \end{array}

\newline

What mistake did he make in combining the rational expressions?

\newline

(A) He forgot to factor the denominator.

\newline

(B) He failed to find a common denominator.

\newline

\newline

(D) He made a mistake in simplifying the numerators.

Identify Common Denominator: Juan starts with the expression $\frac{2}{x-1} + \frac{3}{x+1}$ . He needs to find a common denominator to combine these fractions.
Combine Fractions Incorrectly: Juan attempts to combine the fractions by adding the numerators and denominators separately, resulting in $\frac{2+3}{x-1+x+1}$ . This is incorrect because he cannot simply add the denominators as if they were like terms. The correct method is to find a common denominator, which would be the product of the two distinct denominators, $(x-1)(x+1)$ .