Solve Rational Equations with Variables in the Denominators
First, write the value(s)that make the denominator(s)zero. Then solve the equation.
-$$\frac { 5 } { x + 1 } + \frac { 2 } { x - 1 } = \frac { 4 } { ( x + 1 ) ( x - 1 ) }$$
A) $x \neq - 1,1$; $\varnothing$
B) $x \neq - 1,1 ; \{ 2 \}$
C) $x \neq - 1 ; \{ 1 \}$
D) No restrictions; $\{ 1 \}$

Question

Quizplus · Accepted Answer

The denominators are $x + 1$, $x - 1$, and $(x + 1)(x - 1)$. Setting each denominator equal to zero gives the values that make the denominators zero: $x = -1$ and $x = 1$, hence $x \neq -1, 1$. Solving the equation after finding a common denominator and simplifying does not yield a solution that satisfies the original equation, hence the solution set is empty ($\varnothing$).

Solve Rational Equations with Variables in the Denominators First, Write 5x+1+2x−1=4(x+1)(x−1)\frac { 5 } { x + 1 } + \frac { 2 } { x - 1 } = \frac { 4 } { ( x + 1 ) ( x - 1 ) }x+15​+x−12​=(x+1)(x−1)4​

Solve Rational Equations with Variables in the Denominators
First, Write $\frac { 5 } { x + 1 } + \frac { 2 } { x - 1 } = \frac { 4 } { ( x + 1 ) ( x - 1 ) }$