Introduction To Rational Equations:

In algebra solving rational equation is very simple

,we have few rules to solve any type of equations. Whatever we do on one side of the equation, we must do to the other side also. If you have fractions, we can try to eliminate them by multiplying by the common denominator. If there are quadratics involved in our equations, we must get all the terms to one side with zero on the other.The basic rational expression is in the form of fraction.where there is at least one variable in the denominator.

Solved Example Based on Rational Equation :

Ex 1:Solve '3/x+6=2/(4x)'

Sol:

Step 1: The given equation is

'3/x+6=2/(4x)'

subtracting both sides by '2/(4x)'

'3/x+6-(2/(4x))=(2/(4x))-(2/(4x))'

Step 2: Rearrange the equation.

'3/x-2/(4x)+6=0'

subtracting both sides by 6.

'3/x-2/(4x)+6-6=0-6'

'3/x-2/(4x)=-6'

Step 3: Find the l.c.d(least common denominator) x and 4x

L.C.D=4x

'(12-2)/(4x)=-6'

'10/(4x)=-6'

Step 4:Multiply both sides by 4x.

'10/(4x)xx4x=-6xx4x'

10=-24x

Step 5:Divide both sides by -24

'10/(-24)=(-24x)/(-24)'

'x=-5/12'

The solution is [x=-5/12]

what are linear equations

Example Based on Rational Equation:

Ex 2: Solve 'x/(x-2)+1/(x-4)=2/(x^2-6x+8)'

Sol:

Step 1:first factor the 'x^2-6x+8'

factors=(x-4)(x-2)

Step 2:convert common denominator to all

'(x/(x-2))((x-4)/(x-4))+(1/(x-4))((x-2)/(x-2))=2/((x-2)(x-4))'

'(x^2-4x)/((x-2)(x-4))+(x-2)/((x-2)(x-4))=2/((x-2)(x-4))'

'(x^(2)-4x)+(x-2)=2'

'x^(2)-4x+x-2=2'

'x^(2)-3x-4=0'

'(x-4)(x+1)=0'

'x=4 or x=-1'

If we submit the x=4 in the denominator,it is division by zero,so x=4 is not considerable.

x=-1 is the answer

by: johnharmer

POST COMMENT

What Are The Best Laptop Brands Punjab Is Full Of Multi Cuisine Restaurants Swg Has A Lot Of Scope In The It Sector Holzschlitten San Antonio Steel Distributor Acts According To Demands Top 5 Rules For The Answering Center Agent Know More About Enterprise Architecture & Its Importance Hi Def Lipo Using Vaser Bring This Particular Loss Of Frolic In The Water Garments Significance Of Chief Learning Officer For Organizations Think You Will Likely Want To Show Your Own Introduction To Liters To Cups: Consider This Unique Absence Of Swim Attire