Type a math problem

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Type a math problem

Evaluate

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

$(x−3)(3x+1)3(29x−7) $

Short Solution Steps

\frac{24}{x-3} + \frac{15}{3x+1}

$x−324 +3x+115 $

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}.

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x−3$ and $3x+1$ is $(x−3)(3x+1)$. Multiply $x−324 $ times $3x+13x+1 $. Multiply $3x+115 $ times $x−3x−3 $.

\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)}

$(x−3)(3x+1)24(3x+1) +(x−3)(3x+1)15(x−3) $

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.

Since $(x−3)(3x+1)24(3x+1) $ and $(x−3)(3x+1)15(x−3) $ have the same denominator, add them by adding their numerators.

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

$(x−3)(3x+1)24(3x+1)+15(x−3) $

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

Do the multiplications in $24(3x+1)+15(x−3)$.

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

$(x−3)(3x+1)72x+24+15x−45 $

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

Combine like terms in $72x+24+15x−45$.

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

$(x−3)(3x+1)87x−21 $

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

Expand $(x−3)(3x+1)$.

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

$3x_{2}−8x−387x−21 $

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).

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