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

Pearson Algebra 2 Common Core, 2011 View details

4. Ellipses

Finish the assignment

Continue to next subchapter

Exercise 71 Page 644

Factor the numerator and denominator as much as possible. Cancel out common factors, if possible.

Simplified Expression: x-5/x^2-2x+4
Restrictions: x ≠ - 2

Practice makes perfect

We want to simplify the given rational expression. To do so, we will factor the numerator and denominator as much as possible. Then, we will cancel out any common factors.

x^2-3x-10/x^3+8

▼

Factor the numerator

WriteSum

Write as a sum

x^2-5x+2x-10/x^3+8

FactorOut

Factor out x

x(x-5)+2x-10/x^3+8

FactorOut

Factor out 2

x(x-5)+2(x-5)/x^3+8

FactorOut

Factor out (x-5)

(x-5)(x+2)/x^3+8

▼

Factor the denominator

IdPropAdd

Identity Property of Addition

(x-5)(x+2)/x^3+0+8

Rewrite 0 as 2x^2-2x^2

(x-5)(x+2)/x^3+2x^2-2x^2+8

IdPropAdd

Identity Property of Addition

(x-5)(x+2)/x^3+2x^2-2x^2+0+8

Rewrite 0 as 4x-4x

(x-5)(x+2)/x^3+2x^2-2x^2+4x-4x+8

CommutativePropAdd

Commutative Property of Addition

(x-5)(x+2)/x^3+2x^2-2x^2-4x+4x+8

FactorOut

Factor out x^2

(x-5)(x+2)/x^2(x+2)-2x^2-4x+4x+8

FactorOut

Factor out - 2x

(x-5)(x+2)/x^2(x+2)-2x(x+2)+4x+8

FactorOut

Factor out 4

(x-5)(x+2)/x^2(x+2)-2x(x+2)+4(x+2)

FactorOut

Factor out (x+2)

(x-5)(x+2)/(x+2)(x^2-2x+4)

▼

Simplify

CancelCommonFac

Cancel out common factors

(x-5)(x+2)/(x+2)(x^2-2x+4)

SimpQuot

Simplify quotient

x-5/x^2-2x+4

Finally, we will identify the restrictions on the variables from the denominator of the simplified expression and from any other denominator used. For simplicity, we will use their factored forms. Let's try to factor the denominator using the Quadratic Formula with a= 1, b= - 2, and c= 4.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( - 2)±sqrt(( - 2)^2-4( 1)( 4))/2( 1)

▼

Evaluate right-hand side

NegNeg

- (- a)=a

x=2±sqrt((- 2)^2-4(1)(4))/2(1)

CalcPowProd

Calculate power and product

x=2±sqrt(4-16)/2