SOLUTION: Solving Rational Equations. Solve, and check y/10 = 2/5 + 3/8 -1/3 - 5/4y = 3/4 - 1/6y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solving Rational Equations. Solve, and check y/10 = 2/5 + 3/8 -1/3 - 5/4y = 3/4 - 1/6y      Log On


   

Question 60125: Solving Rational Equations.
Solve, and check
y/10 = 2/5 + 3/8

-1/3 - 5/4y = 3/4 - 1/6y
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solving Rational Equations.
Solve, and check
y/10 = 2/5 + 3/8
The LCD is 40 because 10,5, and 8 all go into 40 evenly. Multiply everything by 40 and watch your denominators fade away.
40%2Ay%2F10=40%2A2%2F5%2B40%2A3%2F8
4%2Ay=8%2A2%2B5%2A3
4y=16%2B15
4y=31
4y%2F4=31%2F4
highlight%28y=31%2F4%29
:
Check:
%2831%2F4%29%2F10=2%2F5%2B3%2F8
31%2F40=16%2F40%2B15%2F40
31%2F40=31%2F40 Yippee, we're right!!!
:
-1%2F3-%285%2F4%29y=3%2F4-%281%2F6%29y
The LCD is 12. 3,4, and 6 all go into 12 evenly. Multiply everything by 12 and the denominators will all be canceled.
12%2A%28-1%2F3%29-12%2A%285y%2F4%29=12%2A%283%2F4%29-12%2A%281%2Ay%2F6%29
4%2A%28-1%29-3%2A%285y%29=3%2A%283%29-2%2A%281%2Ay%29
-4-15y=9-2y
-4-15y%2B15y=9-2y%2B15y
-4=9%2B13y
-4-9=9-9%2B13y
-13=13y
-13%2F13=13y%2F13
highlight%28-1=y%29
:
Check:
-1%2F3-%285%2F4%29%28-1%29=3%2F4-%281%2F6%29%28-1%29
-1%2F3%2B5%2F4=3%2F4%2B1%2F6
-4%2F12%2B15%2F12=9%2F12%2B2%2F12
11%2F12=11%2F12
Happy Calculating!!!