Hello

Algebra Level 1

3 x x a + x ² 3 a x x ² a ² = ? \large \frac { 3x }{ x\ -\ a } \ +\ \frac { x²\ -\ 3ax }{ x²\ -\ a² } \ =\ ?

What's the value of this expression for x = 4 x\ =\ 4 and a = 2 a\ =\ 2 ?

(Decimal form)


The answer is 5.3.

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1 solution

Natan Mendes
Jul 10, 2015

First lets start factoring:

3 x x a + x ( x 3 a ) ( x + a ) ( x a ) \large \frac { 3x }{ x-a } +\frac { x(x-3a) }{ (x+a)(x-a) }

Then:

3 x ( x + a ) + x ² 3 a x ( x + a ) ( x a ) \large \frac { 3x(x+a)+x²-3ax }{ (x+a)(x-a) }

Then:

3 x ² + x ² + 3 a x 3 a x ( x + a ) ( x a ) \large \frac { 3x²+x²+3ax-3ax }{ (x+a)(x-a) }

Then:

4 x ² ( x + a ) ( x a ) \large \frac { 4x² }{ (x+a)(x-a) }

Then:

4 ( 4 ) ² 4 + 2 ( 4 2 ) \large \frac { 4(4)² }{ 4+2(4-2) }

64 12 16 3 \large \frac { 64 }{ 12 } \quad \therefore \quad \frac { 16 }{ 3 }

16 3 = 5.33333 \large \frac { 16 }{ 3 } \quad = \boxed{5.33333 }

Thanks!

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