Mathematics: How can ari simplify the following expression 5/a-3-4/2+1/a-3

How can ari simplify the following expression 5/a-3-4/2+1/a-3

komari0217

01.01.2022

$\frac{12-2a}{a-3}\:\:or\:\: \frac{6\times(2-a)}{a-3}$

Step-by-step explanation:

Given Expression is

$\frac{5}{a-3}-\frac{4}{2}+\frac{1}{a-3}$

Step 1 : Group like terms

∵Like Terms are terms with same variable part here $\frac{1}{a-3}$

$\implies\frac{5}{a-3}+\frac{1}{a-3}-\frac{4}{2}$

Step 2: Simplify like terms

$\implies (5+1)\frac{1}{a-3}-2$

$\implies\frac{6}{a-3}-2$

Step 3: Simplify unlike terms by taking same denominator

$\implies\frac{6}{a-3}-\frac{2}{1}$

here, LCM of both denominator is ( a - 3 )

$\implies\frac{6}{a-3}-(\frac{2}{1}\times\frac{a-3}{a-3})$

$\implies\frac{6}{a-3}-\frac{2(a-3)}{a-3}$

$\implies\frac{6}{a-3}-\frac{2a-6}{a-3}$

Step 4: Simplify as they are like Rationl no.

$\implies\frac{6-(2a-6)}{a-3}$

$\implies\frac{6-2a+6}{a-3}$

$\implies\frac{12-2a}{a-3}\:\:or\:\: \frac{6\times(2-a)}{a-3}$

Therefore, Answer is $\frac{12-2a}{a-3}\:\:or\:\: \frac{6\times(2-a)}{a-3}$

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