Question

Simplify as far as possible:

(2x - 5) - (x - 3) / x^2 - 4

Answer 1

$\: hey \: mate \: here \: is \: your \: answer \:$

GIVEN TO ➡️

$\text{Simplify}$

$\frac{(2x - 5) - (x - 3)}{ {x}^{2} - 4 }$

So Now To Simplify This We Need To Do Following Steps ....

1 )) So First Open Bracket Of Numerator

That is ➡️

$\frac{(2x - 5 )- (x - 3)}{ {x}^{2} - 4} = \frac{(2x - 5 - x + 3)}{ {x}^{2} - 4 }$

2)) Now Solve The Numerator ....

That is ➡️

$\frac{(2x - x - 5 + 3)}{ {x}^{2} - 4 } ( \: re arranged \: terms \: of \: numerator \: )$

Now Combine The Like Terms Of Numerator ....

That is ➡️

$\frac{(x - 2)}{ {x}^{2} - 4 }$

3)) Now We Have Successfully Simplified Numerator Now We Need To Simplify Denominator.....

That is ➡️

$\frac{(x - 2)}{ {x}^{2} - 4 } = \frac{(x - 2)}{ {x}^{2} - {2}^{2} } \: ( \: as \: {x}^{2} = \: {2} \times {2} = {2}^{2} )$

We Know An Identity That Is ➡️

${a}^{2} - {b}^{2} = \: (a + b)(a - b)$

So Now Applying This Identity In Denominator We Have ...

$\frac{(x - 2)}{ {x}^{2} - {2}^{2} } = \frac{(x - 2)}{(x + 2)(x - 2)}$

Now In This Simplified Form We Can Cancel (X-2 ) From Numerator and Denominator

So we have...

$\frac{1}{(x + 2)} \: that \: is \: also \: equal \: to \: {(x + 2)}^{ - 1}$

HENCE THIS IS THE SIMPLIFIED FORM...

$HOPE \: \: IT'S \: \: HELPFUL.$

Be BRAINLY ☯️