### 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}{7x^{2}}+\frac{1}{9xy}\end{equation}

3.

Find the LCM of the denominators and simplify the expression.

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

4.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{6}{x^{3}-343}+\frac{6}{x^{2}-49}\end{equation}

5.

Find the LCM of the denominators and simplify the expression.

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

6.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{18x^{2}}+\frac{1}{27x}+\frac{1}{45x^{3}}\end{equation}

7.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{x^{2}+12x+35}+\frac{1}{(x+5)(x+5)}\end{equation}

8.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{5}{9(x+5)}+\frac{8}{x+5}\end{equation}

9.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{8}+\frac{9x}{10}\end{equation}

10.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{10}{6x}+\frac{4}{6x}\end{equation}

11.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{3x+6}+\frac{1}{6x+6}\end{equation}

12.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{5}{x^{2}}+\frac{x+7}{x+8}\end{equation}

13.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+4}{x+6}+\frac{x+10}{x-6}\end{equation}

14.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{10x}{x^{2}+6x}+\frac{x+8}{x+6}\end{equation}

15.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{8x}{6}-(\frac{3x}{3})\end{equation}

16.

Find the LCM of the denominators and simplify the expression.

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

17.

Find the LCM of the denominators and simplify the expression.

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

18.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{9x}{x+3}-(\frac{7x}{x+4})\end{equation}

19.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{4}{2x^{3}}-(\frac{8}{4x})\end{equation}

20.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{4}{x^{2}+7x}-(\frac{9}{x})\end{equation}

21.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{x^{2}+11x+28}-(\frac{1}{x^{2}-49})\end{equation}

22.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+2}{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}{6(x^{2}+8x)}-(\frac{7}{x^{2}+15x+56})\end{equation}