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

3.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{(x+5)(x+3)}+\frac{1}{(x+5)(x+8)}\end{equation}

4.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{10}{x^{3}-729}+\frac{10}{x^{2}-81}\end{equation}

5.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{7(x+10y)}+\frac{1}{x^{2}+100y^{2}+20xy}\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}+14x+48}+\frac{1}{(x+6)(x+10)}\end{equation}

8.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{2}{10(x+5)}+\frac{6}{x+5}\end{equation}

9.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{2}+\frac{9x}{5}\end{equation}

10.

Find the LCM of the denominators and simplify the expression.

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

11.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{x}{9x+4}+\frac{1}{4x+3}\end{equation}

12.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{7}{x^{2}}+\frac{x+6}{x+9}\end{equation}

13.

Find the LCM of the denominators and simplify the expression.

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

14.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{3x}{x^{2}+5x}+\frac{x+7}{x+5}\end{equation}

15.

Find the LCM of the denominators and simplify the expression.

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

16.

Find the LCM of the denominators and simplify the expression.

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

17.

Find the LCM of the denominators and simplify the expression.

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

18.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{5x}{x+6}-(\frac{3x}{x+7})\end{equation}

19.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{7}{4x^{3}}-(\frac{2}{24x})\end{equation}

20.

Find the LCM of the denominators and simplify the expression.

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

21.

Find the LCM of the denominators and simplify the expression.

\begin{equation}\frac{1}{x^{2}+14x+48}-(\frac{1}{x^{2}-36})\end{equation}

22.

Find the LCM of the denominators and simplify the expression.

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

23.

Find the LCM of the denominators and simplify the expression.

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