Question

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

Answer 1

Answer:

Step-by-step 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.

Answer 2

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

${ \dashrightarrow{ \sf{ \red{ \frac{2(x + 4)(x - 4}{ x(x+6)+4(x+6)}}}}} \\ \\ \\

{ \dashrightarrow{ \sf{ \red{ \frac{2(x + 4)(x - 4)}{(x+6)(x+4)}}}}} \\ \\ \\

{ \dashrightarrow{ \sf{ \red{ \frac{2(x - 4)}{ (x-6)}}}}}$