How do you simplify #\frac { x ^ { 2} + 2x - 8} { x ^ { 2} + x - 6} #?

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Answer 1 · 2018-01-30T23:10:12

See a solution process below:

First, factor the numerator and denominator as:

#((x + 4)(x - 2))/((x + 3)(x - 2))#

Now, cancel common terms in the numerator and denominator:

#((x + 4)color(red)(cancel(color(black)((x - 2)))))/((x + 3)color(red)(cancel(color(black)((x - 2))))) =>#

#(x + 4)/(x + 3)#

However, going back to the original expression, we cannot divide by #0#. Therefore, the solution is:

#(x + 4)/(x + 3)# Where #x + 3 != 0# and #x - 2 != 0#

Or

#(x + 4)/(x + 3)# Where #x != -3# and #x != 2#