Question

Simplify (2x^2-32)/x^2+10+24

Answer 1

`{ \dashrightarrow{ \sf { \red{ \frac{2 {x}^(2) - 32}{ {x}^(2) + 10x + 24}}} } } \\ \\ \\ { \dashrightarrow{ \sf{ \red{ \frac{2( {x}^(2) - 16)}{ {x}^(2) +(6x+4x) +24}}}}} \\ \\ \\ { \dashrightarrow{ \sf{ \red{ \frac{2(x + 4)(x - 4)}{ {x}^(2) + 6x + 4x +24}}}}}`

`{ \dashrightarrow{ \sf{ \red{ (2(x + 4)(x - 4)/( x(x+6)+4(x+6))}}}} \\ \\ \\</p><p></p><p></p><p></p><p>{ \dashrightarrow{ \sf{ \red{ (2(x + 4)(x - 4))/((x+6)(x+4))}}}} \\ \\ \\</p><p></p><p></p><p>{ \dashrightarrow{ \sf{ \red{ (2(x - 4))/( (x-6))}}}}`

Answer 2

Explanation:

(2x^2-32)/(x^2 + 10x + 24) is less subject to misinterpretation. Write these factors in a vertical column:

(2x^2-32)

------------------------- and then factor numerator and denominator separately:

(x^2 + 10x + 24)

2(x^2 - 16) 2(x - 4)(x + 4) 2(x - 4)

--------------------- = --------------------- = ---------------- Note: This is good ONLY

(x + 4)(x + 6) (x + 4)(x + 6) x + 6 for x ≠ -4! Division by

is not defined.