body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Dashboard

Core Connections Algebra 2, 2013 View details

2. Section 3.2

Continue to next subchapter

Exercise 120 Page 159

Practice makes perfect

The fractions we want to add do not have the same denominator. 1/x+2+3/x^2-4 Let's factor x^2-4 to see if we can find a common denominator.

x^2-4

WritePow

Write as a power

x^2-2^2

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(x+2)(x-2)

This means that we can rewrite the expression as follows. 1/x+2+3/(x+2)(x-2) By multiplying the numerator and denominator of the first fraction by (x-2), we will be able to add the fractions and then simplify.

1/x+2+3/(x+2)(x-2)

ExpandFrac

a/b=a * (x-2)/b * (x-2)

x-2/(x+2)(x-2)+3/(x+2)(x-2)

AddFrac

Add fractions

x-2+3/(x+2)(x-2)

AddTerms

Add terms

x+1/(x+2)(x-2)

To find how to rewrite the fractions so that they have the same denominator, let's factor the denominators. In the first fraction we can factor out 2.

3/2x+4-x/x^2+4x+4 [0.7em] ⇕ [-0.2em] 3/2(x+2)-x/x^2+4x+4 In the second fraction let's rewrite 4x to 2x+2x and factor.

x^2+4x+4

▼

Factor

WriteSum

Write as a sum

x^2+2x+2x+4

FactorOut

Factor out x

x(x+2)+2x+4

FactorOut

Factor out 2

x(x+2)+2(x+2)

FactorOut

Factor out (x+2)

(x+2)(x+2)

Therefore, the expression can be written as follows. 3/2(x+2)-x/(x+2)(x+2) By multiplying the first numerator and denominator by (x+2) and the second numerator and denominator by 2, the fractions will have the same denominator. Then we can subtract.

3/2(x+2)-x/(x+2)(x+2)

ExpandFrac

a/b=a * (x+2)/b * (x+2)

3(x+2)/2(x+2)(x+2)-x/(x+2)(x+2)

ExpandFrac

a/b=a * 2/b * 2

3(x+2)/2(x+2)(x+2)-2x/2(x+2)(x+2)

SubFrac

Subtract fractions

3(x+2)-2x/2(x+2)(x+2)

Distr

Distribute 3