Chapter 8: Q. 303 (page 982)

Solve Rational Equations
In the following exercises, solve.
$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ .

Short Answer

Expert verified

The solution for $a$ from the equation $\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ is, $a = 10$

Step by step solution

Step 1. Given information

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ .

We need to solve the given equation.

Step 2.Note any value of the variable that would make any denominator zero.

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}, a \neq 0$ .

Here, the LCD is, $10 a$ .

Multiply the given equation with LCD on both sides.

$10 a (\frac{1}{a} + \frac{2}{5}) = 10 a . \frac{1}{2}$

Distribute the LCD and then simplify it.

role="math" localid="1647850759521" $(\frac{10 a}{a} + \frac{20 a}{5}) = \frac{10 a}{2} 10 + 4 a = 5 a 5 a - 4 a = 10 a = 10$

Step 3. Let us check the answer.

Substitute $a = 10$ in the given equation.

$\frac{1}{a} + \frac{2}{5} = \frac{1}{2} \frac{1}{10} + \frac{2}{5} = \frac{1}{2} \frac{1 + 2 (2)}{10} = \frac{1}{2} \frac{1 + 4}{10} = \frac{1}{2} \frac{5}{10} = \frac{1}{2} \frac{1}{2} = \frac{1}{2}$

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Solve Rational Equations
In the following exercises, solve.
$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2.Note any value of the variable that would make any denominator zero.

Step 3. Let us check the answer.

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Solve Rational EquationsIn the following exercises, solve.1a+25=12.

Short Answer

Step by step solution

Step 1. Given information

Step 2.Note any value of the variable that would make any denominator zero.

Step 3. Let us check the answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Probability and Statistics

Mechanics Maths

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve Rational Equations
In the following exercises, solve.
$\frac{1}{a} + \frac{2}{5} = \frac{1}{2}$ .