## Introductory Algebra for College Students (7th Edition)

Both problems are sums involving common denominators. To add fractions or rational expressions with the same denominator, add numerators and place the sum over the common denominator. Fractions: $\displaystyle \frac{3}{8}+\frac{1}{8}=\frac{4}{8}$ Rational expressions: $\displaystyle \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1}=\frac{x+1}{x^{2}-1}$ Also, both problems have common factors in the numerators and denominators. Both can be reduced: Fractions: $\displaystyle \frac{4}{8}=\frac{4}{4\times 2}=\frac{1}{2}$ Rational expressions: $\displaystyle \frac{x+1}{x^{2}-1}=\frac{(x+1)}{(x+1)(x-1)}=\frac{1}{x-1}$
Both problems are sums involving common denominators. To add fractions or rational expressions with the same denominator, add numerators and place the sum over the common denominator. Fractions: $\displaystyle \frac{3}{8}+\frac{1}{8}=\frac{4}{8}$ Rational expressions: $\displaystyle \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1}=\frac{x+1}{x^{2}-1}$ Also, both problems have common factors in the numerators and denominators. Both can be reduced: Fractions: $\displaystyle \frac{4}{8}=\frac{4}{4\times 2}=\frac{1}{2}$ Rational expressions: $\displaystyle \frac{x+1}{x^{2}-1}=\frac{(x+1)}{(x+1)(x-1)}=\frac{1}{x-1}$