How can you evaluate #(6x-1)/(x^2-25) - (7x-6)/(x^2-25) #?

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Answer 1 · 2015-07-29T07:33:14

#=color(blue)(-1/(x+5)#

#(6x-1)/(x^2-25) - (7x-6)/(x^2-25)#

Here we can combine the numerators of the two terms as the denominators are equal.

#=((6x-1)-(7x-6))/(x^2-25)#

#=((6x-1-7x+6))/(x^2-25)#

#=((6x-7x+6-1))/(x^2-25)#

#=((-x+5))/(x^2-25)#

Now, as per property:
#color(blue)(a^2-b^2 = (a+b)(a-b)#

So, #x^2-25= (x+5)(x-5)#

The expression now becomes
#=((-x+5))/((x+5)(x-5))#

#=(-cancel((x-5)))/((x+5)cancel(x-5))#
#=color(blue)(-1/(x+5)#