Rational Equations Solving Online

Learning equation of the form P(x)/Q(x) over the set of real numbers and Q(x) ≠ 0 where P(x) and Q(x) are two polynomials is called rational equation. Rational equations made easy for learning through online.

Example for rational equations: 3/8 = 3/(d + 4)

(x4 + x3 + x + 1)/(x + 5) = 9/5

1/(x + 9) = 3

12a-6 = 3a-2

Example problem for rational equations solving online:


The following example problems give idea for solving rational equations.

Example 1:

Find x value of the rational equation (6x + 36) / (9x + 54) = 6x

Solution:

Step 1: Given equation

(6x + 36) / (9x + 54) = 6x

Step 2: Take 6 and 9 out as common term from numerator and denominator respectively.

6(x + 6) / 9(x + 6) = 6x

Step 3: Cancel the term (x + 6)

6/9 = 6x

Step 4: Rearrange the above equation,

6/(6 * 9) = x

1/9 = x

x = 1/9

Example 2:

Find out x value for the equation x/(x - 4) + (1/x - 8) = 6/(x2 - 12x + 32)

Solution:

Step 1: Given equation

x/(x - 4) + (1/x - 8) = 6/(x2 - 12x + 32)

Step 2: Replace the term (x2 - 12x + 32) by (x - 4) (x - 8)

x/(x - 4) + (1/x - 8) = 6/ (x - 4) (x - 8)

Step 3: Make common denominator.

(x/(x - 4))((x - 8)/(x - 8)) + ((1/x - 8))((x - 4)/(x -4)) = 6/ (x - 4) (x - 8)

(x2 - 8x) / (x - 4)(x - 8) + (x - 4) / (x - 4)(x - 8) =  6/ (x - 4) (x - 8)

Step 4: Cancel the term (x - 4)(x - 8), we get

(x2 - 8x) + (x - 4) = 6

Step 5: Rearrange the above equation

x2 - 7x - 4 = 6

x2 - 7x - 4 - 6 = 0

x2 - 7x - 10 = 0

Step 6: On factorizing, we get

x = 8.217, - 1.217

This is how the rational equations can be solved through online.


Homework problem for rational equations solving online:


A few homework problems are given below  for solving rational equations.

1) Simplify and find x for the equation (4x + 12)/(4x + 32) = 1/(x + 8)

2) Find x value for the equation 1/(x + 7) = 4

3) Solve and find x for the equation (x2 - 12x + 32)/(x - 8) = 8

Solutions:

1) x = -2

2) x = -5

3) x = 12