Question

How do you simplify \[\dfrac{5}{{x + 3}} - \dfrac{2}{{x - 1}}\]?

Answer 1

Hint: To simplify the expression, at first, we will find the LCM of \[x + 3\] and \[x - 1\] to make into like fractions. Then we will multiply the numerator with the alternate denominators. Next, we will calculate as per the mathematical operators.

Complete step by step answer:
It is given that, \[\dfrac{5}{{x + 3}} - \dfrac{2}{{x - 1}}\]
We have to simplify the given expression.
We have, \[\dfrac{5}{{x + 3}} - \dfrac{2}{{x - 1}}\]
The LCM of \[x + 3\] and \[x - 1\] is\[(x + 3)(x - 1)\].
Simplifying we get,
\[ \Rightarrow \dfrac{{5(x - 1) - 2(x + 3)}}{{(x + 3)(x - 1)}}\]
On multiplication we get,
\[ \Rightarrow \dfrac{{5x - 5 - 2x - 6}}{{(x + 3)(x - 1)}}\]
On adding we get,
\[ \Rightarrow \dfrac{{3x - 11}}{{(x + 3)(x - 1)}}\]
On rewriting we get,
\[ \Rightarrow \dfrac{{3x - 11}}{{{x^2} + 2x - 3}}\]

Hence, \[\dfrac{5}{{x + 3}} - \dfrac{2}{{x - 1}} = \dfrac{{3x - 11}}{{{x^2} + 2x - 3}}\]

Note: An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. They are also termed algebraic equations.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign.
An algebraic expression contains a variable with or without a coefficient, a mathematical operator, and sometimes a constant. The different parts of an algebraic expression are:
Variable: A variable is a letter whose value is unknown. It can take any value depending upon the situation.
Coefficient: The coefficient is a numerical value used before a variable to modify its value. It may or may not be present in an algebraic expression.
Constant: A constant is any term whose value remains unchanged throughout the algebraic expression.
Operator: Mathematical operators are used in an algebraic expression to perform some mathematical calculation on two or more expressions.