How do you simplify #(x^2 - 7x + 10)/( x^2 - 10x + 25) * (x - 5)/( x - 2)#?

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Answer 1 · 2018-06-18T05:55:32

#1#

In questions on algebraic fractions - the first step is to factorise as far as possible.

#(x^2 - 7x + 10)/( x^2 - 10x + 25) * (x - 5)/( x - 2)#

#= ((x-5)(x-2))/((x-5)(x-5)) * ((x - 5))/(( x - 2))#

If you have factors which are all multipied together, then you can cancel like factors.

#= (cancel((x-5))cancel((x-2)))/(cancel((x-5))cancel((x-5))) * (cancel((x - 5)))/(cancel(( x - 2)))#

#=1#

Answer 2 · 2018-06-18T06:06:08

#(x^2-7x+10)/(x^2-10x+25)#.#(x-5)/(x-2)# = #1#

Factorize first:

Step 1: Factorize #x^2-7x+10#

Lets find two numbers or factors, when multiplied, gives #10# and when added together it gives #-7#

#2 xx 5 = 10#

#2 xx -5 = -10#

#-2 xx -5 = 10# -----> This is the one!

Re-write the equation:

#x^2-2x-5x+10#

#x(x-2)-5(x-2)#

#(x-2)(x-5)#

Step 2: Factorize #x^2-10x+25#

Lets find two numbers or factors, when multiplied, gives #25# and when added together it gives #-10#

#5 xx 5 = 25#

#5 xx -5 = -25#

#-5 xx -5 = 25# -----> This is the one!

Re-write the equation:

#x^2-5x-5x+25#

#x(x-5)-5(x-5)#

#(x-5)(x-5)#

Lets write the whole equation with the factors we got above and then simplify further.

#(x^2-7x+10)/(x^2-10x+25)#.#(x-5)/(x-2)# = #((x-2)(x-5))/((x-5)(x-5))#.#(x-5)/(x-2)#

#(cancel(x-2)cancel(x-5))/(cancel(x-5)cancel(x-5))#.#cancel(x-5)/cancel(x-2)# = #1#

Answer is #1#