Write the partial fraction decomposition of the rational expression. $\frac { 1 } { y ( q - y ) }$
A) $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q + y } \right)$
B) $\frac { 1 } { q } \left( \frac { 1 } { y } - \frac { 1 } { q - y } \right)$
C) $\frac { 1 } { y } + \frac { 1 } { q - y }$
D) $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q - y } \right)$
E) $\frac { 1 } { q } \left( - \frac { 1 } { y } - \frac { 1 } { q - y } \right)$

Question

Write the partial fraction decomposition of the rational expression.​ $\frac { 1 } { y ( q - y ) }$ ​
A) $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q + y } \right)$
B) $\frac { 1 } { q } \left( \frac { 1 } { y } - \frac { 1 } { q - y } \right)$
C) $\frac { 1 } { y } + \frac { 1 } { q - y }$
D) $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q - y } \right)$
E) $\frac { 1 } { q } \left( - \frac { 1 } { y } - \frac { 1 } { q - y } \right)$

Quizplus · Accepted Answer

The correct partial fraction decomposition of $\frac{1}{y(q-y)}$ is $\frac{1}{q}\left(\frac{1}{y} + \frac{1}{q-y}\right)$, which matches option D. This is because when you decompose the fraction, you separate it into parts that sum back to the original expression, and the coefficients are determined by solving the equation for the constants that make the decomposition equal to the original fraction.

Write the Partial Fraction Decomposition of the Rational Expression 1y(q−y)\frac { 1 } { y ( q - y ) }y(q−y)1​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 1 } { y ( q - y ) }$