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


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}.

Answer and Explanation: 1

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Given that {eq}\displaystyle \frac{y}{{(y + 4)(2y - 1)}} = \frac{A}{{y + 4}} + \frac{B}{{2y - 1}} {/eq}.

This gives


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Learn more about this topic:

Partial Fractions: Rules, Formula & Examples


Chapter 3 / Lesson 26

Learn about what partial fractions are and their formula. Understand the method of how to do partial fractions from the rational and improper functions.

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