Write the partial fraction decomposition of the rational expression.Check your result algebraically. $$\frac { 5 } { x ^ { 2 } + 5 x }$$
A) $\frac { A } { x } + \frac { B } { x - 5 }$
B) $\frac { 1 } { x } - \frac { 1 } { x + 5 }$
C) $\frac { 1 } { x } + \frac { 1 } { x + 5 }$
D) $\frac { A } { x } - \frac { B } { x - 5 }$
E) $\frac { 1 } { x } - \frac { 1 } { x - 5 }$

Question

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $$\frac { 5 } { x ^ { 2 } + 5 x }$$ ​
A) $\frac { A } { x } + \frac { B } { x - 5 }$
B) $\frac { 1 } { x } - \frac { 1 } { x + 5 }$
C) $\frac { 1 } { x } + \frac { 1 } { x + 5 }$
D) $\frac { A } { x } - \frac { B } { x - 5 }$
E) $\frac { 1 } { x } - \frac { 1 } { x - 5 }$

Quizplus · Accepted Answer

The given expression can be factored as $\frac{5}{x(x+5)}$. The partial fraction decomposition of this expression is $\frac{A}{x} + \frac{B}{x+5}$. To find the values of A and B, we set up the equation $5 = A(x+5) + Bx$. Solving this equation for A and B gives $A = 1$ and $B = -1$, leading to the decomposition $\frac{1}{x} - \frac{1}{x+5}$.

Write the Partial Fraction Decomposition of the Rational Expression 5x2+5x\frac { 5 } { x ^ { 2 } + 5 x }x2+5x5​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 } { x ^ { 2 } + 5 x }$