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Chapter 7: Q. 185 (page 681)

Simplify a Complex Rational Expression by Using the LCD.

In the following exercises, simplify each complex rational expression by using the LCD.

mm+54+1m-5

Short Answer

Expert verified

The simplification is m2-5m4m2+m-95.

Step by step solution

01

Step 1. Given. 

The given complex rational expression is: mm+54+1m-5.

02

Step 2. To find 

We have to simplify each complex rational expression by using the LCD.

03

Step 3. Calculation 

LCM of the denominators is =(m+5)(m-5). Multiply numerator and denominator by it to simplify.

mm+54+1m-5=mm+5(m+5)(m-5)4(m+5)(m-5)+1m-5(m+5)(m-5)=m(m-5)4(m+5)(m-5)+(m+5)=m2-5m4(m2-25)+m+5=m2-5m4m2-100+m+5=m2-5m4m2+m-95

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