Previously we have discussed about length of an arc calculator and In this session I am going to tell you about the subtraction in rational expressions which comes under state board of secondary education andhra pradesh. Before starting the topic we must know about the rational numbers. The Rational numbers can be any numbers that can be represented in a form of fraction say a/b where a is the numerator that can be any integer and b is the denominator that is a whole or non zero number. For instance: 2/3, 4/5 etc.

While subtracting rational numbers, we need to convert denominators to a common denominator; otherwise we cannot solve the problem. Now here is the method by which we can solve such problems in mathematics:

Subtract 8/10x – 2/5x

First take LCM of 10 and 5, so that we can get the LCD.

10: 2*5

5: 1*5

So the LCM is 2*5 that is 10. So 10 is also the common denominator.

(8x – (2*2)*x) / 10x (Subtract)

4x/10x (Simplify the term by dividing both the denominator and numerator by 2)

2/5 (answer)

One more example:

Subtract [x/(x - 1)] – [1/x] (Take LCM to get LCD).

[x*x – (x - 1)] / [(x - 1)*x](Simplify each term).

(X2 – x – 1) / (x2 - x)

In the next session, we will learn about Rationalizing the Denominator

and if anyone want to know about Solving Multi Step Inequalities then they can refer to Internet and text books for understanding it more precisely.

While subtracting rational numbers, we need to convert denominators to a common denominator; otherwise we cannot solve the problem. Now here is the method by which we can solve such problems in mathematics:

1. First find out the common denominator.

2. To find common denominator, first find the LCM (lcm calculator) that is Least Common Multiple of all the denominators. We can use the listing method for this, where we can list all the multiples of all the denominators until we find a number that exist in all the lists.

3. After finding LCD (Least Common Denominator), proceed to the subtraction.

4. Now make the lowest term of the resultant term and put it into the answer.

We can understand this by solving problems related to the**rational expressions subtractions**. Here is an example for this.(want to Learn more about Rational Expressions, click here),Subtract 8/10x – 2/5x

First take LCM of 10 and 5, so that we can get the LCD.

10: 2*5

5: 1*5

So the LCM is 2*5 that is 10. So 10 is also the common denominator.

(8x – (2*2)*x) / 10x (Subtract)

4x/10x (Simplify the term by dividing both the denominator and numerator by 2)

2/5 (answer)

One more example:

Subtract [x/(x - 1)] – [1/x] (Take LCM to get LCD).

[x*x – (x - 1)] / [(x - 1)*x](Simplify each term).

(X2 – x – 1) / (x2 - x)

In the next session, we will learn about Rationalizing the Denominator

and if anyone want to know about Solving Multi Step Inequalities then they can refer to Internet and text books for understanding it more precisely.

Rational numbers addition and subtraction are very nicely solved,but I think it becomes complicated and hard to learn,as we know maths require more practice so here is an simple definition of rational number for learners-Rational numbers can be whole numbers, fractions, and decimals. They can be written as a ratio of two integers in the form a/b where a and b are integers and b nonzero.

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