Evaluate

\frac{3\left(29x-7\right)}{\left(x-3\right)\left(3x+1\right)}

$(x−3)(3x+1)3(29x−7) $

Factor

\frac{3\left(29x-7\right)}{\left(x-3\right)\left(3x+1\right)}

$(x−3)(3x+1)3(29x−7) $

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\frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)}+\frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x+1 is \left(x-3\right)\left(3x+1\right). Multiply \frac{24}{x-3} times \frac{3x+1}{3x+1}. Multiply \frac{15}{3x+1} times \frac{x-3}{x-3}.

\frac{24\left(3x+1\right)+15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}

Since \frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)} and \frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)} have the same denominator, add them by adding their numerators.

\frac{72x+24+15x-45}{\left(x-3\right)\left(3x+1\right)}

Do the multiplications in 24\left(3x+1\right)+15\left(x-3\right).

\frac{87x-21}{\left(x-3\right)\left(3x+1\right)}

Combine like terms in 72x+24+15x-45.

\frac{87x-21}{3x^{2}-8x-3}

Expand \left(x-3\right)\left(3x+1\right).