Your Algebra Homework Can Now Be Easier Than Ever!

Solving Rational Equations

A rational equation is an equation that involves one or more rational expressions. For example,
the equation is a rational equation.

To solve a rational equation, the denominators can be eliminated by multiplying each side of the
equation by the LCD of all of the rational expressions in the equation .

The steps are :
1. De termine the LCD of all of the rational expressions in the equation.
2. Multiply each side of the equation by the LCD.
3. Use the distributive law so that each in dividual expression is multiplied by the LCD.
4. Simplify by dividing out common factors.
5. Solve the resulting equation.
6.
Check the answer(s) in the original equation. This is very important because it is
possible to find a solution for the equation in step #5 that is not a solution of the original
equation. This happens if the value found in step #5 makes one or more of the
denominators of the original equation equal to zero .

1. Use the steps given above to solve each of the fol lowing equations . For each equation,
first write down the LCD.

2. Let . Find all values of a such that f (a) =1.

3. Summary :
The LCD ( least common denominator) is used when adding or subtracting rational expressions
and when solving rational equations.

When the LCD is used in adding or subtracting rational expressions, the numerator and
denominator
of each fraction must be multiplied only by the factors that are necessary to turn the
denominator into the LCD. That is, compare each denominator to the LCD and then multiply
both the numerator and denominator of that fraction by the factors in the LCD that are missing
from that denominator.

When the LCD is used in solving rational equations, multiply the entire left side and the entire
right side of each equation by the LCD. This will result in each term being multiplied by the
LCD. If the LCD has been chosen correctly, each fraction in the equation can then be reduced
and the new equation should contain no fractions. Remember that it is very important to check
your answer or answers in the original equation since extraneous solutions might be obtained.

Keeping these guidelines in mind, add, subtract, or solve as indicated.

(a) Subtract:

(b) Solve:

Answers

1.
(a) x = 3
(b) t = 2, t = 5
(c) No solutions

2. a = -3/2, a = 2

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 December 12th 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 © 2004-2017, Algebra-Answer.Com.  All rights reserved.