Question

What is the simplified form of $\dfrac{{{x^2} - 25}}{{x - 5}}$?

Answer 1

Hint: This problem is based on the algebraic expressions and identities. To simplify this we will use the formula $a^2-b^2=(a-b)(a+b)$ in the numerator. After doing some mathematical operations, we will get the required answer.

Complete step-by-step answer:
The given algebraic expression in the question is$\dfrac{{{x^2} - 25}}{{x - 5}}$.
We need to use the above formula to reduce the term ${x^2} - 25$.
Now, ${x^2} - 25$ can be written as ${x^2} - {5^2}$.
In this term, we can observe that $a = x$ and $b = 5$.
Substituting the values of $a$ and $b$ in the formula, we get,
${x^2} - 25 = (x + 5)(x - 5)$ .
Hence, the expression becomes as follows.
$\dfrac{{{x^2} - 25}}{{x - 5}} = \dfrac{{(x + 5)(x - 5)}}{{x - 5}}$
On canceling the common terms on the numerator and the denominator in the above expression, we get,
$\dfrac{{{x^2} - 25}}{{x - 5}} = x + 5$, which is the required solution.
Therefore, the simplified form of $\dfrac{{{x^2} - 25}}{{x - 5}}$is \[x + 5\].

Note: Simplification of an expression is the process of changing the expression effectively without changing the meaning of an expression.
In this question we need to apply the BODMAS rule (i.e.) we need to calculate the brackets first and then orders, then division or multiplication, and finally we need to add or subtract.
Moreover, various steps are involved to simplify an expression. Some of the steps are listed below:
If the given expression contains like terms, we need to combine them.
Example: $3x + 2x + 4 = 5x + 4$
We need to split an expression into factors (i.e) the process of finding the factors for the given expression.
Example: ${x^2} + 4x + 3 = (x + 3)(x + 1)$
We need to expand an algebraic expression (i.e) we have to remove the respective brackets of an expression.
Example: $3(a + b) = 3a + 3b$.
We need to cancel out the common terms in an expression.