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Chapter 8: Q. 324 (page 982)

In the following exercises, solve.

3r+10-4r-4=1

Short Answer

Expert verified

The answer isr=-3,-4.

Step by step solution

01

Step 1. Given Information

A radical expression is given as

3r+10-4r-4=1

02

Step 2. Clearing the fractions

The least common denominator is (r-4)(r+10)

Multiply the equation by LCD,

localid="1647779805341" (r+10)(r-4)3r+10-4r-4=1(r+10)(r-4)(r-4)(3)-{4(r+10)}=r2-4r+10r-403r-12-{4r+40)=r2+6r-403r-12-4r-40=r2+6r-40r2+7r+12=0

03

Step 3. Solution of the equation

Now, solving the quadratic equation,

r2+7r+12=0r2+3r+4r+12=0r(r+3)+4(r+3)=0(r+4)(r+3)=0

Using the Zero product property,

r+4=0r=-4r+3=0r=-3

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