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

2 Answers
Jun 18, 2018

1

Explanation:

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

Jun 18, 2018

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

Explanation:

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