Your Algebra Homework Can Now Be Easier Than Ever!

Multiplying and Dividing Rational Expressions

Questions

1. Simplify

2. Simplify

3. Simplify

4. Simplify

5. Simplify

6. Simplify

7. Simplify

Solutions

1. Simplify Factor all polynomials :

x2 + 3x − 10 = (x − 2)(x + 5) two numbers whose product is −10 sum is 3: −2, 5
x2 − 3x − 4 = (x − 4)(x + 1) two numbers whose product is −4 sum is −3: −4, 1
x2 + x − 20 = (x + 5)(x − 4) two numbers whose product is −20 sum is 1: −4, 5
x2 + 4x + 3 = (x + 3)(x + 1) two numbers whose product is 3 sum is 4: 1, 3

Simplify polynomial multiplication .

and x − 4 ≠ 0, x + 1 ≠ 0, x + 5 ≠ 0

2. Simplify Factor all polynomials :

x2 − x − 20 = (x − 5)(x + 4) two numbers whose product is −20 sum is −1: −5, 4
x2 − 3x − 10 = (x − 5)(x + 2) two numbers whose product is −10 sum is −3: −5, 2
x2 + 7x + 10 = (x + 5)(x + 2) two numbers whose product is 10 sum is 7: 5, 2
x2 + 4x − 5 = (x + 5)(x − 1) two numbers whose product is −5 sum is 4: 5,−1

Simplify polynomial multiplication .

and x + 5 ≠ 0, x − 5≠ 0, x + 2 ≠ 0

3. Simplify Factor all polynomials:

6x2 + 17x + 10
= 6x2 + 12x + 5x + 10 two numbers whose product is 60 sum is 17: 12, 5
= 6x(x + 2) + 5(x + 2) Factor by grouping
= (6x + 5)(x + 2)

36x2 − 25 = (6x − 5)(6x + 5) Difference of squares

Simplify polynomial division .

Simplify polynomial multiplication.

and 6x + 5 ≠ 0, 6x − 5 ≠ 0

4. Simplify Factor all polynomials:

4x2 + 12x + 9
= 4x2 + 6x + 6x + 9 two numbers whose product is 36 sum is 12: 6, 6
= 2x(2x + 3) + 3(2x + 3) Factor by grouping
= (2x + 3)(2x + 3) hey–this was a perfect square !

4x2 − 9 = (2x + 3)(2x − 3) Difference of squares
6x − 9 = 3(2x − 3) common factor

Simplify polynomial division .

Simplify polynomial multiplication .

and 2x − 3 ≠ 0, 2x + 3 ≠ 0

5. Simplify Factor all polynomials (let the y tag along with the constants):

3x2 + 12xy + 12y2
= 3x2 + 6xy + 6xy + 12y2 two numbers whose product is 36 sum is 12: 6, 6
= 3x(x + 2y) + 6y(x + 2y) Factor by grouping
= (3x + 6y)(x + 2y) = 3(x + 2y)(x + 2y) hey–this was a perfect square !

x2 + 4xy + 3y2 = (x + 1y)(x + 3y) = (x + y)(x + 3y) two numbers whose product is 3 sum is 4: 1, 3
4x + 8y = 4(x + 2y) common factor

Simplify polynomial division .

Simplify polynomial multiplication.

and x + 2y ≠ 0, x + y ≠ 0

6. Simplify Factor all polynomials:

5y2 + 17y + 6
= 5y2 + 15y + 2y + 6 two numbers whose product is 30 sum is 17: 15, 2
= 5y(y + 3) + 2(y + 3) Factor by grouping
= (5y + 2)(y + 3)

10y2 + 9y + 2
= 10y2 + 5y + 4y + 2 two numbers whose product is 20 sum is 9: 5, 4
= 5y(2y + 1) + 2(2y + 1) Factor by grouping
= (5y + 2)(2y + 1)

2y2 + 5y − 3 = 2y2 + 6y − 1y − 3 two numbers whose product is −6 sum is 5: 6,−1
= 2y(y + 3) − 1(y + 3) Factor by grouping
= (2y − 1)(y + 3)

4y2 − 1 = (2y − 1)(2y + 1) difference of squares

Simplify polynomial multiplication .

and 5y + 2 ≠ 0, y + 3 ≠ 0, 2y + 1 ≠ 0, 2y − 1 ≠ 0

7. Simplify Factor all polynomials:

x2 + 8x + 15 = (x + 5)(x + 3) two numbers whose product is 15 sum is 8: 5, 3

2x2 + 11x + 5
= 2x2 + 10x + 1x + 5 two numbers whose product is 10 sum is 11: 10, 1
= 2x(x + 5) + 1(x + 5) Factor by grouping
= (2x + 1)(x + 5)

2x2 − 7x − 4
= 2x2 − 8x + 1x − 4 two numbers whose product is −8 sum is −7: −8, 1
= 2x(x − 4) + 1(x − 4) Factor by grouping
= (2x + 1)(x − 4)

x2 + 6x + 9 = (x + 3)(x + 3) two numbers whose product is 9 sum is 6: 3, 3

Simplify polynomial division .

Simplify polynomial multiplication .

and x + 5 ≠ 0, x + 3 ≠ 0, 2x + 1 ≠ 0
 

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of March 28th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2024, Algebra-Answer.Com.  All rights reserved.