SOLUTION: simplify the complex fraction 5/6y^2/3/9y^3, 3/x-1/x+3/2/x+5/x+3 How do you do these?

Algebra ->  Algebra  -> Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: simplify the complex fraction 5/6y^2/3/9y^3, 3/x-1/x+3/2/x+5/x+3 How do you do these?       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Numeric Fractions Solvers Lessons Answers archive Quiz In Depth

 Question 171512: simplify the complex fraction 5/6y^2/3/9y^3, 3/x-1/x+3/2/x+5/x+3 How do you do these? Answer by ptaylor(2052)   (Show Source): You can put this solution on YOUR website!OK. Here's how you do complex fractions: Lets look at the complex fraction (a/b)/(c/d). Now if we can make the denominator (c/d) of this complex fraction equal to 1, then we will have a simple fraction. We can do this by multiplying both the numerator and denominator by (d/c). When we do this, we get: ((a/b)*(d/c))/((c/d)*(d/c)); simplifying we have: (ad/bc)/1 or ad/bc. Now lets apply this to your specific problem: (5/6y^2)/(3/9y^3); multiply numerator and denominator by (9y^3/3): ((5/6y^2)*(9y^3/3))/((3/9y^3)(9y^3/3)) and we get (45y^3)/(18y^2)/1 cancel and simplify and we have: 5y/2 For the second part. It is sometimes good to use parens to better clarify the problem: 3/x-1/x+3/2/x+5/x+3= (3/(x-1)/(x-3))/(2/(x+5)/(x+3)) Now here we have both the numerator and denominator as complex fractions: We'll do the numerator first: (3/(x-1)/(x-3))= (3*(x-3)/(x-1))/((x-1)/(x-3))*(x-3)/(x-1))= 3(x-3)/(x-1)/1=3(x-3)/(x-1) Now the denominator: (2/(x+5)/(x+3))= (2*(x+3)/(x+5))/((x+5)/(x+3)*(x+3)/(x+5))= 2(x+3)/(x+5) Now we put the numerator and denominator back together and we still have a complex fraction: (3(x-3)/(x-1))/(2(x+3)/(x+5))= (3(x-3)/(x-1))*(x+5)/2(x+3))/(2(x+3)/(x+5))*(x+5)/2(x+3))= (3(x-3)(x+5))/(2(x+3)(x-1)) Actually, using the little formula that we worked out initially: (a/b)/(c/d)=ad/bc, you can determine the a, b , c & d of your problem and simply plug the values in. For example, look at the numerator that we worked out above: (3/(x-1)/(x-3)); a=3 b=1 c=(x-1) d=(x-3) now pluggin in (ad/bc), we have 3(x-3)/1(x-1) which is what we got before. Hope this helps---ptaylor