Let's reduce: <math><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo> + </mo><mn>2</mn><mi>x</mi><mo> + </mo><mn>1</mn></mrow><mrow><mi>x</mi><mo> + </mo><mn>1</mn></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>2</mn></mrow></msup><mo> + </mo><mn>2</mn><mi>x</mi><mo> + </mo><mn>1</mn></math>
You can rephrase the expression into: <math><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math>
With the new factorized numerator, we try to simplify the new quotient: <math><mfrac><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>x</mi><mo> + </mo><mn>1</mn></mrow></mfrac></math>

▷<b>Result: &nbsp; <math><mi>x</mi><mo> + </mo><mn>1</mn></math></b><span style='font-size:smaller'> &nbsp; &nbsp; (processing: 5 steps, 2 ms)</span>