Solving rational equations?

Question

3 = -2/4 + 4/2y so I have 4 and 2y as the denominators. The Algebra software program I am using gives the common denominator as 4y. How can that be if y is not common to both, 4 is common to both but not y.
thanks

Answer 1

you can reduce the 1st term to -1/2 .... that allows you to use 2y as a common denom....


think of it like this ....if you multiply each term by 4y, you remove the denominators....then it looks easier

3(4y) = (4y) -2/4 + (4y) 4/2y

12y = -2y + 8
14y = 8
y = (4 / 7)


check ...
3= -1/2 + 4 / 2(4/7)
3 = -1/2 + 4 / (8/7)
3 1/2 = 4 (7/8)
3 1/2 = 28 / 8 ...........this checks

Answer 2

The common denominator is a "new" denominator which contains all other denominators. 4y contains 2 (2*2), 4, and y

In the equation
3 = -2/4 + 4/2y
to get a denominator common to both fractions you must multiply the first by (y/y) and the 2nd by (2/2)

3 = (-2/4)(y/y) + (4/2y)(2/2)
3 = -2y/4y + 8/4y
Now the fractions can be added to get
3 = (8 - 2y)/4y

Answer 3

Well, this could be solved only by taking common denominators, but as you said y, which is in the denominator cannot be taken as common. So, for this purpose, we provide a y in the first term by multiplying y both in the numerator and denominator.

So, you get 4y as common denominator and solve it like this:
3 = (-2y + 8 ) / 4y

12y = -2y + 8

14y = 8

y = 14 / 8 = 7 / 4

y = 7/4

Answer 4

The common denominator isn't common to both. It's the other way around.

Each denominator has to be a factor OF the common denominator.

2 divides evenly into 4y, with the leftover factors of 2y
and
2y divides evently into 4y, with the leftover factor of 2.

Just imagine if that y had been a 3.
Your two denominators would have been 4 and 6 ... the common denominator would have been 12.

Answer 5

The common denominator is created using both existing denominators.

= -2 / 4 = -2 *(y) / 4*(y)
= - 2y / 4y

Answer 6

common denominator is based 100% on the denominator (the numbers on bottem)

if you multiply both top and bottem of each fraction by the same number in your equation it will remain equal.
However, if you are trying to solve the equation, your goal is to isolate the variable, y. the common denominator isn't going to help you do that (since y is on the bottom of a fraction, a good first step would be multiplying both sides by y to get it on top).

Answer 7

common denominator is a multiple of the denominators