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\frac{\left(x+2\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x+2 is \left(x+1\right)\left(x+2\right). Multiply \frac{x+2}{x+1} times \frac{x+2}{x+2}. Multiply \frac{x+1}{x+2} times \frac{x+1}{x+1}.
\frac{\left(x+2\right)\left(x+2\right)-\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}
Since \frac{\left(x+2\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+2x+2x+4-x^{2}-x-x-1}{\left(x+1\right)\left(x+2\right)}
Do the multiplications in \left(x+2\right)\left(x+2\right)-\left(x+1\right)\left(x+1\right).
\frac{2x+3}{\left(x+1\right)\left(x+2\right)}
Combine like terms in x^{2}+2x+2x+4-x^{2}-x-x-1.
\frac{2x+3}{x^{2}+3x+2}
Expand \left(x+1\right)\left(x+2\right).
\frac{\left(x+2\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x+2 is \left(x+1\right)\left(x+2\right). Multiply \frac{x+2}{x+1} times \frac{x+2}{x+2}. Multiply \frac{x+1}{x+2} times \frac{x+1}{x+1}.
\frac{\left(x+2\right)\left(x+2\right)-\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}
Since \frac{\left(x+2\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+2x+2x+4-x^{2}-x-x-1}{\left(x+1\right)\left(x+2\right)}
Do the multiplications in \left(x+2\right)\left(x+2\right)-\left(x+1\right)\left(x+1\right).
\frac{2x+3}{\left(x+1\right)\left(x+2\right)}
Combine like terms in x^{2}+2x+2x+4-x^{2}-x-x-1.
\frac{2x+3}{x^{2}+3x+2}
Expand \left(x+1\right)\left(x+2\right).