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\frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+5\right)}-\frac{x\left(x+5\right)}{\left(x+1\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+5 and x+1 is \left(x+1\right)\left(x+5\right). Multiply \frac{x+1}{x+5} times \frac{x+1}{x+1}. Multiply \frac{x}{x+1} times \frac{x+5}{x+5}.
\frac{\left(x+1\right)\left(x+1\right)-x\left(x+5\right)}{\left(x+1\right)\left(x+5\right)}
Since \frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+5\right)} and \frac{x\left(x+5\right)}{\left(x+1\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+x+x+1-x^{2}-5x}{\left(x+1\right)\left(x+5\right)}
Do the multiplications in \left(x+1\right)\left(x+1\right)-x\left(x+5\right).
\frac{-3x+1}{\left(x+1\right)\left(x+5\right)}
Combine like terms in x^{2}+x+x+1-x^{2}-5x.
\frac{-3x+1}{x^{2}+6x+5}
Expand \left(x+1\right)\left(x+5\right).
\frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+5\right)}-\frac{x\left(x+5\right)}{\left(x+1\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+5 and x+1 is \left(x+1\right)\left(x+5\right). Multiply \frac{x+1}{x+5} times \frac{x+1}{x+1}. Multiply \frac{x}{x+1} times \frac{x+5}{x+5}.
\frac{\left(x+1\right)\left(x+1\right)-x\left(x+5\right)}{\left(x+1\right)\left(x+5\right)}
Since \frac{\left(x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x+5\right)} and \frac{x\left(x+5\right)}{\left(x+1\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+x+x+1-x^{2}-5x}{\left(x+1\right)\left(x+5\right)}
Do the multiplications in \left(x+1\right)\left(x+1\right)-x\left(x+5\right).
\frac{-3x+1}{\left(x+1\right)\left(x+5\right)}
Combine like terms in x^{2}+x+x+1-x^{2}-5x.
\frac{-3x+1}{x^{2}+6x+5}
Expand \left(x+1\right)\left(x+5\right).