Solve: $\frac { 5 } { x + 7 } - \frac { 4 } { x + 2 } = \frac { 3 x } { x ^ { 2 } + 9 x + 14 }$
A) {19}
B) {-9}
C) {-19}
D) {9}

Question

Quizplus · Accepted Answer

The equation can be simplified by recognizing that the denominator on the right side, $x^2 + 9x + 14$, factors into $(x + 7)(x + 2)$. This allows us to combine the fractions on the left side over a common denominator, $(x + 7)(x + 2)$, and equate it to the right side. Solving the resulting equation leads to the solution $x = -9$.

Solve 5x+7−4x+2=3xx2+9x+14\frac { 5 } { x + 7 } - \frac { 4 } { x + 2 } = \frac { 3 x } { x ^ { 2 } + 9 x + 14 }x+75​−x+24​=x2+9x+143x​

Solve $\frac { 5 } { x + 7 } - \frac { 4 } { x + 2 } = \frac { 3 x } { x ^ { 2 } + 9 x + 14 }$