Home > Algebra > Clearing Denominators in Rational Equations

How do you simplify #\frac { 9x + 81} { 4x ^ { 3} } \cdot \frac { x } { x ^ { 2} - 81}#?

Answer 1

#(9)/((4x^2)(x-9))#

Let's use our "cross-simplify" method. Let's factor if there is any factorable part there. We see that #9x+81=9(x+9)# and #x^2-81=(x+9)(x-9)# Therefore, we now have: #(9(x+9))/(4x^3)*x/((x-9)(x+9))# We rewrite #4x^3# as #4x*x*x# #(9(x+9))/(4x*x*x)*x/((x-9)(x+9))# Now, remember that #(a*b*c)/(d*e)*d/(b*b)=(a*cancelb*c)/(canceld*e)*canceld/(cancelb*b)#

Therefore, #(9cancel(x+9))/(4cancelx*x*x)*cancelx/((x-9)cancel(x+9))# So we now have:#(9)/(4x^2)*1/((x-9))=>(9)/((4x^2)(x-9))# That is our answer!

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.