An equation which has rational expression is known as rational equation. A fraction is also termed as a rational equation. By certain steps we can solve the rational equations. We can practice many problems through online. We are going to see some problems to practice the rational equations.
Example: `1/x` + `5/x` = `7/9` is a rational expression called rational equation.
Explanation to Rational Equations Practice
The following steps are helpful for solving the Rational Expressions.
Step 1:
If possible factor the denominator of every rational expression term in rational equation.
Step 2:
Be sure that the rational expressions in rational equation has same denominator. If not, make it by taking LCM for all rational expression.
Step 3:
Now cancelling all the common terms and simplifying for final answer.
Example Problems to Rational Equations Practice:
Example: 1
Solve: `1/6` = `x/8`
Solution:
Given,
`1/6` = `x/8`
Step 1:
1 × 8 = 6 x
Step 2:
6 x = 8
x = `8/6`
x = `4/3`
Answer: x = `4/3`
Example: 2
Solve: `x/8` + `5/8` = `7/8`
Solution:
Given: `x/8` + `5/8` = `7/8`
Step 1:
The fractions `x/8` , `5/8` and `7/8` having a common factor 8 in their denominator.
Step 2:
`x/8` + `5/8` = `7/8`
`(x + 5)/8` = `7/8`
Step 3:
Cancel a common factor 8 on both sides of above rational equation.
x + 5 = 7
x + 5 - 5 = 7 - 5
x = 2
Answer: x = 2
Example: 3
Solve: `6/x` + `8/(x + 3)` = `(10)/(x^2 + 3x)`
Solution:
Given,on: `6/x` + `8/(x + 3)` = `(10)/(x^2 + 3x)`
Step 1:
Factor the last rational expression `10/(x^2 + 3x)` = `10/(x(x +3))`
Step 2:
LCM of the all the terms in given rational equation is x(x + 3)
`6/x` x `(x + 3)/(x + 3)` = `(6(x + 3)) /(x(x + 3))`
`8/(x+ 3) ` x `x/x` = `(8x)/(x(x+3))`
`(10)/(x^2 +3x)` x `1/1` = `(10)/(x(x + 3))`
Step 3:
Now the rational equation is,
`"(6(x + 3))/(x(x+3))` + `(8x)/(x(x+3))` = `(10)/(x(x+3))`
`(6x + 18 + 8x)/(x(x+3))` = `(10)/(x(x+3))`
Step 4:
By cancelling the common x(x + 3) we get,
6x + 18 + 8x = 10
14x + 18 = 10
14x = 10 - 18
14x = -8
x = -`8/14`
x = `-4/7`
Answer: x = `-4/7`.
Practice Problem to Rational Equations Practice:
Problem: 1
Solve: `6/x` = `5/6`
Answer: x = `36/5`
Problem: 2
Solve the rational equation, `(x -9)/5` = `21/9`
Answer: x = `62/3`
Example: `1/x` + `5/x` = `7/9` is a rational expression called rational equation.
Explanation to Rational Equations Practice
The following steps are helpful for solving the Rational Expressions.
Step 1:
If possible factor the denominator of every rational expression term in rational equation.
Step 2:
Be sure that the rational expressions in rational equation has same denominator. If not, make it by taking LCM for all rational expression.
Step 3:
Now cancelling all the common terms and simplifying for final answer.
Example Problems to Rational Equations Practice:
Example: 1
Solve: `1/6` = `x/8`
Solution:
Given,
`1/6` = `x/8`
Step 1:
1 × 8 = 6 x
Step 2:
6 x = 8
x = `8/6`
x = `4/3`
Answer: x = `4/3`
Example: 2
Solve: `x/8` + `5/8` = `7/8`
Solution:
Given: `x/8` + `5/8` = `7/8`
Step 1:
The fractions `x/8` , `5/8` and `7/8` having a common factor 8 in their denominator.
Step 2:
`x/8` + `5/8` = `7/8`
`(x + 5)/8` = `7/8`
Step 3:
Cancel a common factor 8 on both sides of above rational equation.
x + 5 = 7
x + 5 - 5 = 7 - 5
x = 2
Answer: x = 2
Example: 3
Solve: `6/x` + `8/(x + 3)` = `(10)/(x^2 + 3x)`
Solution:
Given,on: `6/x` + `8/(x + 3)` = `(10)/(x^2 + 3x)`
Step 1:
Factor the last rational expression `10/(x^2 + 3x)` = `10/(x(x +3))`
Step 2:
LCM of the all the terms in given rational equation is x(x + 3)
`6/x` x `(x + 3)/(x + 3)` = `(6(x + 3)) /(x(x + 3))`
`8/(x+ 3) ` x `x/x` = `(8x)/(x(x+3))`
`(10)/(x^2 +3x)` x `1/1` = `(10)/(x(x + 3))`
Step 3:
Now the rational equation is,
`"(6(x + 3))/(x(x+3))` + `(8x)/(x(x+3))` = `(10)/(x(x+3))`
`(6x + 18 + 8x)/(x(x+3))` = `(10)/(x(x+3))`
Step 4:
By cancelling the common x(x + 3) we get,
6x + 18 + 8x = 10
14x + 18 = 10
14x = 10 - 18
14x = -8
x = -`8/14`
x = `-4/7`
Answer: x = `-4/7`.
Practice Problem to Rational Equations Practice:
Problem: 1
Solve: `6/x` = `5/6`
Answer: x = `36/5`
Problem: 2
Solve the rational equation, `(x -9)/5` = `21/9`
Answer: x = `62/3`
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