Solution:
We have been asked to find the simplified expression of
[tex] 3/4x+3+21/8x^2-14x-15=\frac{3}{4x+3} +\frac{21}{8x^2-14x-15}\\
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\text{We will have to make the denominator equal to add}\\
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\
8x^2-14x-15=8x^2+6x-20x-15\\
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\
=2x(4x+3)-5(4x+3)=(4x+3)(2x-5)\\
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\frac{3}{4x+3} +\frac{21}{8x^2-14x-15}=\frac{3}{4x+3} +\frac{21}{(4x+3)(2x-5)}\\
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=\frac{3(2x-5)+21}{(4x+3)(2x-5)}\\
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=\frac{6x-15+21}{(4x+3)(2x-5)} \\
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=\frac{6x+6}{(4x+3)(2x-5)} \\ [/tex]
