What is the sum of the rational expression: (3x + 2)/(x – 1) + (2x – 5)/(x – 1)?

Geometry is the branch of mathematics that deals with figures and dimensions, arithmetic is the branch of mathematics that deals with numbers and operations, similarly, algebra is also the branch of mathematics that deals with numerals and variables. The term that has a constant value is known as numerals and represented by numbers. The term that does not have a constant value is known as variables and is represented by letters and symbols.

Algebraic Expression

An algebraic expression is the combination of numerals and variables with basic mathematical operators. Generally, the mathematical statement is written in form of algebraic expression with the help of numerals and variables. For example, 9 is subtracted from a number that can be written as ‘x-9’. Here we do not have any fixed value of the number so we suppose it as x. Minus sign separates the statement into two terms. So on the basis of the number of terms, the algebraic expression can be classified into the following categories:

• Monomial: If the number of terms in an expression is one then it is known as a monomial. Example: 8t, 9y, etc.
• Binomial: If the number of terms in an expression is two then it is known as the binomial. Example: 8x – 8t, 8t + 3, etc
• Trinomial: If the number of terms in an expression is three then it is known as trinomial. Example: 5a + 2b +3c, 5q -9r +2t, etc.
• Polynomial: If the number of terms in an expression is one or more than one then it is known as a polynomial.

Like and unlike terms

If the variable part of two or more terms of an expression is the same then these terms are known as the like terms and if the variable part of two or more terms of the expression is not the same then these terms are known as unlike terms. We do all the operations on the like terms.

For example:  5x³ – 3x² + 2 – x + 2x² – 9x

In the above expression, 3x³ and 2x², -x and -9x are like terms.

What is the sum of the rational expression: (3x + 2)/(x – 1) + (2x – 5)/(x – 1)?

Solution:

Step to solve the problem:

Step 1: Figure out if the terms of the expression are in like fractions or not. If the denominator of the two or more fractions is the same then it is known as the like terms. 

We can see in the given question denominator is (x – 1), so they are in like fractions.

Step 2: Apply the operation on the numerator part of the like part of the fraction.

= (3x + 2)/(x – 1) + (2x – 5)/(x – 1)

= (3x + 2 + 2x – 5)/(x – 1)

= (5x -3)/(x – 1)

Sum of the rational expressions (3x + 2)/(x – 1) + (2x – 5)/(x – 1) is (5x -3)/(x – 1).

Similar Questions

Question 1: What is the sum of the rational expressions: (5x + 2)/(x + 4) + (2x – 5)/(x + 4)

Solution:

In the given problem the denominator of both the term is the same, so they are like terms. Just simply do the operation on the numerator.

= (5x + 2 +2x – 5)/(x + 4)

Add the like terms.

= (7x – 3)/(x + 4)

Question 2: What is the sum of the rational expressions: (5y – 9)/(3x + 2) + (2y +3)/(3x + 2)

Solution:

In the given problem the denominator of both the term is the same, so they are like terms. Just simply do the operation on the numerator.

= (5y – 9 + 2y +3)/(3x + 2)

Add or subtract the like terms.

= (7y – 6)/(3x + 2)

Question 3: What is the sum of the rational expressions: (y – 8)/(7x + 1) + (4y + 7)/(7x + 1)

Solution:

In the given problem the denominator of both the term is the same, so they are like terms. Just simply do the operation on the numerator.

= (y – 8 + 4y + 7)/(7x + 1) 

Now Add or subtract the like terms and we get,

= (5y – 1)/(7x + 1)