### 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.

\begin{equation}\frac{1}{x}+\frac{1}{y}\end{equation}

2.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{10x^{2}}+\frac{1}{7xy}\end{equation}

3.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{(x+5)(x+4)}+\frac{1}{(x+5)(x+6)}\end{equation}

4.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{9}{x^{3}-729}+\frac{9}{x^{2}-81}\end{equation}

5.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{9(x+4y)}+\frac{1}{x^{2}+16y^{2}+8xy}\end{equation}

6.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{4x^{2}}+\frac{1}{6x}+\frac{1}{10x^{3}}\end{equation}

7.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{x^{2}+10x+24}+\frac{1}{(x+6)(x+8)}\end{equation}

8.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{10}{3(x+8)}+\frac{2}{x+8}\end{equation}

9.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{10}+\frac{5x}{2}\end{equation}

10.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{6}{6x}+\frac{10}{8x}\end{equation}

11.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{9x+2}+\frac{1}{2x+9}\end{equation}

12.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{4}{x^{2}}+\frac{x+3}{x+8}\end{equation}

13.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+10}{x+6}+\frac{x+10}{x-6}\end{equation}

14.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{3x}{x^{2}+5x}+\frac{x+4}{x+5}\end{equation}

15.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{4x}{4}-(\frac{5x}{10})\end{equation}

16.

Find the LCM of the denominators and simplify the expression.

\begin{equation}8-(\frac{8}{x+6})\end{equation}

17.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+9}{x+2}-(\frac{x+8}{x-2})\end{equation}

18.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{10x}{x+4}-(\frac{3x}{x+4})\end{equation}

19.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{3}{9x^{3}}-(\frac{7}{45x})\end{equation}

20.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{5}{x^{2}+9x}-(\frac{4}{x})\end{equation}

21.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{x^{2}+10x+21}-(\frac{1}{x^{2}-9})\end{equation}

22.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+8}{x^{2}-25}-(\frac{1}{25-x^{2}})\end{equation}

23.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{5(x^{2}+10x)}-(\frac{8}{x^{2}+14x+40})\end{equation}