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        "name": "3_6 Partial Fractions",
        "intro": "<h4>Introduction<\/h4>\n<p>It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions. For example it can be shown that <span class=\"math inline\">\\[\\dfrac{4x+7}{x^2+3x+2}\\]<\/span>&nbsp;has the same value as <span class=\"math inline\">\\[\\dfrac{1}{x+2} +\\dfrac{3}{x+1}\\]<\/span>&nbsp;for any value of <span class=\"math inline\">\\(x\\)<\/span>. We say that <span class=\"math inline\">\\( \\dfrac{4x+7}{ x^2+3x+2}\\) <b> is identically equal to <\/b> \\(\\dfrac{1}{ x+2} + \\dfrac{3}{ x+1}\\)<\/span> and that the <span><strong>partial fractions<\/strong><\/span> of <span class=\"math inline\">\\(\\dfrac{4x+7}{ x^2+3x+2}\\)<\/span> are <span class=\"math inline\">\\(\\dfrac{1}{ x+2}\\)<\/span> and <span class=\"math inline\">\\(\\dfrac{3}{ x+1}\\)<\/span>. The ability to express a fraction as its partial fractions is particularly useful in the study of Laplace transforms, <span class=\"math inline\">\\(Z\\)<\/span>-transforms, Control Theory and Integration. In this Section we explain how partial fractions are found.<\/p>\n<br>",
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