Chapter 8: Q 199 (page 953)

Add $\frac{2 y}{y + 3} + \frac{3}{y - 1}$ .

Short Answer

Expert verified

The sum is $\frac{2 y^{2} + y + 9}{(y + 3) (y - 1)}$ .

Step by step solution

Given Information

The Given expression is $\frac{2 y}{y + 3} + \frac{3}{y - 1}$ .

Find the LCD of denominators.

Since there are no common factors in denominators.

The LCD is $(y + 3) (y - 1)$ .

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{2 y (y - 1)}{(y + 3) (y - 1)} + \frac{3 (y + 3)}{(y + 3) (y - 1)}$

Simplify numerator.

$= \frac{2 y^{2} - 2 y}{(y + 3) (y - 1)} + \frac{3 y + 9}{(y + 3) (y - 1)}$

Add and simplify the numerator.

Take common denominator.

$= \frac{2 y^{2} - 2 y + 3 y + 9}{(y + 3) (y - 1)}$

$= \frac{2 y^{2} + y + 9}{(y + 3) (y - 1)}$

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Add $\frac{2 y}{y + 3} + \frac{3}{y - 1}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Add and simplify the numerator.

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Add2yy+3+3y-1.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Add and simplify the numerator.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Applied Mathematics

Geometry

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Add $\frac{2 y}{y + 3} + \frac{3}{y - 1}$ .