### 10.5 Least Common Multiple, Add/Subtract: Unlike Denominators

Problem #

Problem Statement

Problems Similar To

1.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{x}+\frac{1}{y}$$

2.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{7x^{2}}+\frac{1}{9xy}$$

3.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{(x+6)(x+8)}+\frac{1}{(x+6)(x+2)}$$

4.

Find the LCM of the denominators and simplify the expression.

$$\frac{6}{x^{3}-343}+\frac{6}{x^{2}-49}$$

5.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{4(x+3y)}+\frac{1}{x^{2}+9y^{2}+6xy}$$

6.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{18x^{2}}+\frac{1}{27x}+\frac{1}{45x^{3}}$$

7.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{x^{2}+12x+35}+\frac{1}{(x+5)(x+5)}$$

8.

Find the LCM of the denominators and simplify the expression.

$$\frac{5}{9(x+5)}+\frac{8}{x+5}$$

9.

Find the LCM of the denominators and simplify the expression.

$$\frac{x}{8}+\frac{9x}{10}$$

10.

Find the LCM of the denominators and simplify the expression.

$$\frac{10}{6x}+\frac{4}{6x}$$

11.

Find the LCM of the denominators and simplify the expression.

$$\frac{x}{3x+6}+\frac{1}{6x+6}$$

12.

Find the LCM of the denominators and simplify the expression.

$$\frac{5}{x^{2}}+\frac{x+7}{x+8}$$

13.

Find the LCM of the denominators and simplify the expression.

$$\frac{x+4}{x+6}+\frac{x+10}{x-6}$$

14.

Find the LCM of the denominators and simplify the expression.

$$\frac{10x}{x^{2}+6x}+\frac{x+8}{x+6}$$

15.

Find the LCM of the denominators and simplify the expression.

$$\frac{8x}{6}-(\frac{3x}{3})$$

16.

Find the LCM of the denominators and simplify the expression.

$$5-(\frac{5}{x+6})$$

17.

Find the LCM of the denominators and simplify the expression.

$$\frac{x+4}{x+9}-(\frac{x+2}{x-9})$$

18.

Find the LCM of the denominators and simplify the expression.

$$\frac{9x}{x+3}-(\frac{7x}{x+4})$$

19.

Find the LCM of the denominators and simplify the expression.

$$\frac{4}{2x^{3}}-(\frac{8}{4x})$$

20.

Find the LCM of the denominators and simplify the expression.

$$\frac{4}{x^{2}+7x}-(\frac{9}{x})$$

21.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{x^{2}+11x+28}-(\frac{1}{x^{2}-49})$$

22.

Find the LCM of the denominators and simplify the expression.

$$\frac{x+2}{x^{2}-25}-(\frac{1}{25-x^{2}})$$

23.

Find the LCM of the denominators and simplify the expression.

$$\frac{1}{6(x^{2}+8x)}-(\frac{7}{x^{2}+15x+56})$$