HA2 Adding and Subtracting Rational Expressions Practice

HA2 Adding and Subtracting Rational Expressions Practice

How to Add/Subtract Rational Expressions

• If possible, rewrite the denominators as factors to see what they have in common.

• Find the LCD (Least Common Denominator)

• Get both fractions to have a common denominator, then COMBINE the numerators and keep the denominator the same.

• Don't forget to distribute the negative in subtraction signs

Multiple Choice

Simplify the expression

• 6x / 20xy

• 3 / 10y

• (6x+1) / (20xy)

• 3 / 20xy

Multiple Choice

Simplify the expression

• n / 2m

• n / 3m

• (m² + 4n²) / 12m

• n / 4m

Multiple Choice

Multiple Choice

Subtract

 $\frac{x-5}{3x+4}-\frac{3x-5}{3x+4}$  

•  $\frac{-2x-10}{3x+4}\ ,\ -\frac{4}{3}$  

•  $\frac{-2x}{3x+4}\ ,\ x\ne-\frac{4}{3}$  

•  $-2x\ ,\ x\ne0$  

•  $-2x-10\ ,\ x\ne0$  

Multiple Choice

Multiple Choice

Add

 $\frac{2x}{x^2-36}+\frac{x+4}{x+6}$  

•  $\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$  

•  $\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$  

•  $\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$  

•  $\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$  

Multiple Choice

Subtract

 $\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$  

•  $\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$  

•  $\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$  

•  $\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$  

•  $\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$  

Multiple Choice

Simplify (Add & Divide)

 $\frac{\frac{1}{2x}+\frac{2}{3x}}{\frac{x-1}{x-3}}$  

•  $\frac{7x-21}{6x^2-6x}\ ,\ x\ne0,\ 1,\ 3$  

• A $\frac{7x-21}{6x^2-6x}\ ,\ x\ne1,\ 3$  

•  $\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne0\ ,\ 1,\ 3$  

•  $\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne1,\ 3$  

Multiple Choice

Add

 $\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$  

•  $\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$  

•  $\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$  

•  $\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$  

•  $\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$