Answer:
[tex]\frac{12-2a}{a-3}\:\:or\:\: \frac{6\times(2-a)}{a-3}[/tex]
Step-by-step explanation:
Given Expression is
[tex]\frac{5}{a-3}-\frac{4}{2}+\frac{1}{a-3}[/tex]
Step 1 : Group like terms
∵Like Terms are terms with same variable part here [tex]\frac{1}{a-3}[/tex]
[tex]\implies\frac{5}{a-3}+\frac{1}{a-3}-\frac{4}{2}[/tex]
Step 2: Simplify like terms
[tex]\implies (5+1)\frac{1}{a-3}-2[/tex]
[tex]\implies\frac{6}{a-3}-2[/tex]
Step 3: Simplify unlike terms by taking same denominator
[tex]\implies\frac{6}{a-3}-\frac{2}{1}[/tex]
here, LCM of both denominator is ( a - 3 )
[tex]\implies\frac{6}{a-3}-(\frac{2}{1}\times\frac{a-3}{a-3})[/tex]
[tex]\implies\frac{6}{a-3}-\frac{2(a-3)}{a-3}[/tex]
[tex]\implies\frac{6}{a-3}-\frac{2a-6}{a-3}[/tex]
Step 4: Simplify as they are like Rationl no.
[tex]\implies\frac{6-(2a-6)}{a-3}[/tex]
[tex]\implies\frac{6-2a+6}{a-3}[/tex]
[tex]\implies\frac{12-2a}{a-3}\:\:or\:\: \frac{6\times(2-a)}{a-3}[/tex]
Therefore, Answer is [tex]\frac{12-2a}{a-3}\:\:or\:\: \frac{6\times(2-a)}{a-3}[/tex]
