For a polynomial of the form <math><mstyle displaystyle="true"><mi>a</mi><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> , rewrite the middle term as a sum of two terms whose product is <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>c</mi><mo>=</mo><mn>5</mn><mo>⋅</mo><mo>-</mo><mn>3</mn><mo>=</mo><mo>-</mo><mn>15</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>14</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>14</mn><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>14</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> plus <math><mstyle displaystyle="true"><mn>15</mn></mstyle></math>

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> .

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

Factor <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>15</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mi>x</mi><mrow><mo>(</mo><mo>-</mo><mn>5</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mn>5</mn><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Reorder terms.

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Do you know how to Simplify (5x^2+14x-3)/(3x-15x^2)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.