First, write the value(s) that make the denominator(s) zero. Then solve the equation.
-$$\frac { 36 } { x - 7 } + 4 = \frac { 4 } { x - 7 }$$
A) $x \neq 7 ; \{ - 1 \}$
B) $x \neq - 7 ; \{ - 1 \}$
C) $x \neq - 7 ; \{ 17 \}$
D) $x \neq 7 ; \varnothing$

Question

Quizplus · Accepted Answer

The denominator $x - 7$ becomes zero when $x = 7$, so $x \neq 7$. To solve the equation, subtract $\frac{4}{x-7}$ from both sides to get $\frac{36}{x-7} = 0$, which simplifies to $36 = 0$, an impossibility, indicating no solution ($\varnothing$). However, the correct process to solve the equation after combining like terms is to multiply both sides by $x - 7$ to eliminate the denominator, leading to $36 + 4(x - 7) = 4$, which simplifies and solves to $x = -1$, indicating an error in explanation but the choice correctly identifies $x \neq 7$ and the solution set $\{-1\}$.

First, Write the Value(s) That Make the Denominator(s) Zero 36x−7+4=4x−7\frac { 36 } { x - 7 } + 4 = \frac { 4 } { x - 7 }x−736​+4=x−74​

First, Write the Value(s) That Make the Denominator(s) Zero $\frac { 36 } { x - 7 } + 4 = \frac { 4 } { x - 7 }$