Question 81393
1. Simplify the rational expression:
x^2 – 6x + 5
Can be factored to:
(x-5)(x-1)
:
x^2 – 25
This is the difference of squares, can be factored to:
(x-5)(x+5)
:
:
2. Divide:
{{{(x^2-9x+8)/(x^2-1)}}}
:
{{{((x-8)(x-1))/((x-1)(x+1))}}} = {{{((x-8))/((x+1))}}}; canceled the (x-1)'s
:
{{{(2x-4)/(2x+2)}}}
:
Factor out 2 and you have:
{{{(2(x-2))/(2(x+1))}}} = {{{(x-2)/(x+1)}}}; canceled 2
:
:
3. Simplify:
√[64x10y2z46]; I can't decipher what you mean here


4. Perform the indicated operations:
{{{4sqrt(18) + 2sqrt(32) - sqrt(8)}}}
:
Factor to show the squares inside the radicals, then extract the sqrts
{{{4sqrt(9*2) + 2sqrt(16*2) - sqrt(4*2)}}} = {{{4*3*sqrt(2) + 2*4*sqrt(2) - 2*sqrt(2)}}} = {{{12*sqrt(2) + 8*sqrt(2) - 2*sqrt(2)}}}
:
Notice we have like terms (all sqrt(2)) so we can just add them up:
{{{18*sqrt(2)}}}; the final result