# Find the value of B in the partial fraction decomposition \frac{y}{(y+4)(2y-1)} = \frac{A}{y + 4}...

## Question:

Find the value of {eq}B {/eq} in the partial fraction decomposition {eq}\frac{y}{(y+4)(2y-1)} = \frac{A}{y + 4} + \frac{B}{2y-1} {/eq}.

## Partial Fraction:

The partial fraction is a method which breaks out a fraction into a more simple fraction. Suppose we have {eq}\displaystyle f\left( x \right) = \frac{{h\left( x \right)}}{{{g_1}\left( x \right){g_2}\left( x \right)}} {/eq}, where {eq}\displaystyle g_1,\; g_2,\; h {/eq} are the polynomial of {eq}\displaystyle x {/eq}. If there exists some polynomial, say, {eq}\displaystyle h_1,\; h_2 {/eq} such that {eq}\displaystyle f\left( x \right) = \frac{{h\left( x \right)}}{{{g_1}\left( x \right){g_2}\left( x \right)}} = \frac{{{h_1}\left( x \right)}}{{{g_1}\left( x \right)}} + \frac{{{h_2}\left( x \right)}}{{{g_2}\left( x \right)}} {/eq}, then {eq}\displaystyle \frac{{{h_1}\left( x \right)}}{{{g_1}\left( x \right)}} + \frac{{{h_2}\left( x \right)}}{{{g_2}\left( x \right)}} {/eq} is known as the partial fraction of {eq}\displaystyle f {/eq}.