Algebra-1 Problems

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}{4x^{2}}+\frac{1}{6xy}\end{equation}

3.

Find the LCM of the denominators and simplify the expression.

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

4.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{2}{x^{3}-125}+\frac{2}{x^{2}-25}\end{equation}

5.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{8(x+7y)}+\frac{1}{x^{2}+49y^{2}+14xy}\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}+18x+81}+\frac{1}{(x+9)(x+5)}\end{equation}

8.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{6}{9(x+10)}+\frac{2}{x+10}\end{equation}

9.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{7}+\frac{4x}{4}\end{equation}

10.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{9}{4x}+\frac{10}{8x}\end{equation}

11.

Find the LCM of the denominators and simplify the expression.

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

12.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{4}{x^{2}}+\frac{x+9}{x+4}\end{equation}

13.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+9}{x+10}+\frac{x+7}{x-10}\end{equation}

14.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{7x}{x^{2}+4x}+\frac{x+8}{x+4}\end{equation}

15.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{6x}{6}-(\frac{10x}{8})\end{equation}

16.

Find the LCM of the denominators and simplify the expression.

\begin{equation}8-(\frac{8}{x+4})\end{equation}

17.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+9}{x+2}-(\frac{x+6}{x-2})\end{equation}

18.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{10x}{x+8}-(\frac{8x}{x+7})\end{equation}

19.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{2}{3x^{3}}-(\frac{5}{9x})\end{equation}

20.

Find the LCM of the denominators and simplify the expression.

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

21.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{x^{2}+15x+54}-(\frac{1}{x^{2}-36})\end{equation}

22.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x+6}{x^{2}-16}-(\frac{1}{16-x^{2}})\end{equation}

23.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{8(x^{2}+2x)}-(\frac{10}{x^{2}+12x+20})\end{equation}