Question 201757
# 1 



{{{((x^2-9x+8)/(2x-4))/((x^2-1)/(2x+2))}}} Start with the given expression.



{{{((x^2-9x+8)/(2x-4))((2x+2)/(x^2-1))}}} Multiply the first fraction {{{(x^2-9x+8)/(2x-4)}}} by the reciprocal of the second fraction {{{(x^2-1)/(2x+2)}}}.



{{{(((x-1)*(x-8))/(2x-4))((2x+2)/(x^2-1))}}} Factor {{{x^2-9x+8}}} to get {{{(x-1)*(x-8)}}}.



{{{(((x-1)*(x-8))/(2(x-2)))((2x+2)/(x^2-1))}}} Factor {{{2x-4}}} to get {{{2(x-2)}}}.



{{{(((x-1)*(x-8))/(2(x-2)))((2(x+1))/(x^2-1))}}} Factor {{{2x+2}}} to get {{{2(x+1)}}}.



{{{(((x-1)(x-8))/(2(x-2)))((2(x+1))/((x-1)*(x+1)))}}} Factor {{{x^2-1}}} to get {{{(x-1)*(x+1)}}}.



{{{(2(x-1)(x-8)(x+1))/(2(x-2)(x-1)*(x+1))}}} Combine the fractions. 



{{{(highlight(2)highlight((x-1))(x-8)highlight((x+1)))/(highlight(2)(x-2)highlight((x-1))highlight((x+1)))}}} Highlight the common terms. 



{{{(cross(2)cross((x-1))(x-8)cross((x+1)))/(cross(2)(x-2)cross((x-1))cross((x+1)))}}} Cancel out the common terms. 



{{{(x-8)/(x-2)}}} Simplify. 



So {{{((x^2-9x+8)/(2x-4))/((x^2-1)/(2x+2))}}} simplifies to {{{(x-8)/(x-2)}}}.



In other words, {{{((x^2-9x+8)/(2x-4))/((x^2-1)/(2x+2))=(x-8)/(x-2)}}}



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# 2




{{{4*sqrt(50)+sqrt(32)-sqrt(18)}}} Start with the given expression



{{{4*5*sqrt(2)+sqrt(32)-sqrt(18)}}} Simplify {{{sqrt(50)}}} to get {{{5*sqrt(2)}}}. Note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>.



{{{4*5*sqrt(2)+4*sqrt(2)-sqrt(18)}}} Simplify {{{sqrt(32)}}} to get {{{4*sqrt(2)}}}.



{{{4*5*sqrt(2)+4*sqrt(2)-3*sqrt(2)}}} Simplify {{{sqrt(18)}}} to get {{{3*sqrt(2)}}}.



{{{20*sqrt(2)+4*sqrt(2)-3*sqrt(2)}}} Multiply 4 and 5 to get 20.

 


{{{(20+4-3)sqrt(2)}}} Factor out the GCF {{{sqrt(2)}}}



{{{21*sqrt(2)}}} Combine like terms.



So {{{4*sqrt(50)+sqrt(32)-sqrt(18)}}} simplifies to {{{21*sqrt(2)}}}. 



In other words,  {{{4*sqrt(50)+sqrt(32)-sqrt(18)=21*sqrt(2)}}}