To divide by a fraction, multiply by its reciprocal.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>6</mn><mi>u</mi><mo>+</mo><mn>72</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn><mi>u</mi><mo>+</mo><mn>24</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6</mn><mi>u</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mn>3</mn><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mrow><mo>(</mo><mn>36</mn><mo>)</mo></mrow></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mi>u</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>24</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mi>u</mi><mo>+</mo><mn>2</mn><mo>⋅</mo><mn>12</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mi>u</mi><mo>+</mo><mn>36</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mi>u</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mi>u</mi><mo>+</mo><mn>3</mn><mo>⋅</mo><mn>12</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mi>u</mi><mo>+</mo><mn>12</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>96</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mn>20</mn></mstyle></math> .

Write the factored form using these integers.

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>108</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> .

Write the factored form using these integers.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>u</mi><mo>+</mo><mn>12</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>u</mi><mo>+</mo><mn>8</mn></mrow><mrow><mi>u</mi><mo>+</mo><mn>9</mn></mrow></mfrac></mstyle></math> .

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