simplify (x^3-x)/x
Let's simplify: <math><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo> -</mo><mi>x</mi></mrow><mrow><mi>x</mi></mrow></mfrac></math> We first try to factorize the numerator Let's factor in <math><mi>ℝ</mi></math>: <math><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo> -</mo><mi>x</mi></math> You can factorize this expression into: <math><mi>x</mi><mo>·</mo><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo> -</mo><mn>1</mn><mo>)</mo></math> Let's factorize in <math><mi>ℝ</mi></math>: <math><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo> -</mo><mn>1</mn><mo>)</mo></math> <u>Factors found</u>: <math><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo> -</mo><mn>1</mn><mo>)</mo></math> With the new factorized numerator, we try to simplify the new quotient: <math><mfrac><mrow><mi>x</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo> -</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>x</mi></mrow></mfrac></math> <math><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo> -</mo><mn>1</mn><mo>)</mo></math> <math></text><text><mi>x</mi><mo>·</mo><mi>x</mi></text><text><mo> + </mo><mi>x</mi><mo>·</mo><mn>-1</mn></text><text><mo> + </mo><mn>1</mn><mo>·</mo><mi>x</mi></text><text><mo> + </mo><mn>1</mn><mo>·</mo><mn>-1</mn></text><text></math> <math></text><text><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></text><text><mo> -</mo><mi>x</mi></text><text><mo> + </mo><mi>x</mi></text><text><mo> -</mo><mn>1</mn></text><text></math> <math><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo> + </mo><mn>0</mn><mo> -</mo><mn>1</mn></math> ▷<b>Answer: <math><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo> -</mo><mn>1</mn></math></b><span style='font-size:smaller'> (computation took 11 steps and 2 ms)</span>
