Lois C. answered • 04/22/20
BA in secondary math ed with 20+ years of classroom experience
To simplify, we need to cancel out any common factors. To do this, we need both the numerator and denominator to be written in factored. So we begin with the numerator: the GCF is 3, giving us 3(x2 - 25), which, because of the difference of two squares here, further factors into 3(x+5)(x-5).
The denominator almost matches one of the factors in the numerator, except that the order of subtraction is reversed. Any time this happens, you can use what I call the "Negative 1 Trick" where you factor out a -1 from both terms, then switch the order of the terms. It looks like this: 5-x becomes -1(-5 + x). Since -5 + x is the same as x - 5, the entire denominator can be rewritten as -1( x - 5), and we are now able to cancel out the common factor of x - 5 from both numerator and denominator. This then leaves you with 3(x+5)/-1 or, more simply, -3( x + 5 ).
