Question

How do you simplify $ \dfrac{{45}}{{10a - 10}}? $

Answer 1

Hint: Here we will take the given mathematical expressions and will first of all find the common factors and then its multiple to divide or to remove from the numerator and the denominator and then will simplify for the resultant required value.

Complete step by step solution:
Take the given mathematical expression: $ \dfrac{{45}}{{10a - 10}} $
Since there are two terms in the denominator part of the expression, take out a common factor outside the bracket.
 $ \dfrac{{45}}{{10a - 10}} = \dfrac{{45}}{{10(a - 1)}} $
Find out the prime factors of the terms in the numerator and the denominator.
Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ $ 2 $ is the prime number as it can have only $ 1 $ factor.
 $ \dfrac{{45}}{{10a - 10}} = \dfrac{{3 \times 3 \times 5}}{{2 \times 5(a - 1)}} $
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \dfrac{{45}}{{10a - 10}} = \dfrac{{3 \times 3}}{{2(a - 1)}} $
Simplify the above expression –
 $ \dfrac{{45}}{{10a - 10}} = \dfrac{9}{{2(a - 1)}} $
This is the required solution.
So, the correct answer is “$\dfrac{9}{{2(a - 1)}} $”.

Note: Always remember that common factors are removed from the numerator and the denominator when the term is taken from both the terms and specially when the terms are separated from positive or negative signs.