Chapter 8: Q. 316 (page 982)

In the following exercises, solve.
$\frac{3}{t - 6} = \frac{1}{t}$

Short Answer

Expert verified

The solution of the equation $\frac{3}{t - 6} = \frac{1}{t}$ is

$t = - 3$

Step by step solution

Step 1. Given information

The given equation is

$\frac{3}{t - 6} = \frac{1}{t}$

Step 2. Solution of equation

Terms of the equation are not defined for $t = 6 & t = 0$

sorole="math" localid="1647800509525" $\frac{3}{t - 6} = \frac{1}{t}, t \neq 6, t \neq 0$

The least common denominator of all denominators in the equation is $t (t - 6)$

multiply both sides of the equation by the least common denominator $t (t - 6)$

role="math" localid="1647800645888" $t (t - 6) (\frac{3}{t - 6}) = t (t - 6) (\frac{1}{t}) t (3) = (t - 6) (1) 3 t = t - 6 t = - 3$

So the solution of the equation is role="math" localid="1647800631368" $t = - 3$

Step 3. Verification

Substitute $t = - 3$ in the equation

$\frac{3}{t - 6} = \frac{1}{t} \frac{3}{(- 3) - 6} \overset{?}{=} \frac{1}{(- 3)} \frac{3}{- 9} \overset{?}{=} \frac{1}{- 3} \frac{1}{- 3} = \frac{1}{- 3}$

The left-hand side is equal to the right-hand side so the solution is correct.

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In the following exercises, solve.
$\frac{3}{t - 6} = \frac{1}{t}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solution of equation

Step 3. Verification

One App. One Place for Learning.

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In the following exercises, solve.3t-6=1t

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solution of equation

Step 3. Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Geometry

Applied Mathematics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$\frac{3}{t - 6} = \frac{1}{t}$