how do you solve this?

Question

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

((1)/(3g^2)) , ((3)/(2g^5))

please give an answer, but also show how you worked it out!

Answer 1

Hi,

Factor each denominator into primes. Write each denominator as its prime factors to the power it occurs. The least common denominator will need each prime factor to the highest power that it has in any denominator.

For your problem, you want the LCM of 3g² and 2g^5, factor everything into primes:

3g² = 3*g²
2g^5 = 2*g^5

The LCD needs 2, 3, and g, each to its highest power. This makes the LCD 2 * 3 *g^5 or 6g^5.

Let's look at other examples.

If you have denominators of 24 and 28, they factor as follows:

24 = 2³ x 3
28 = 2² x 7

The LCD needs 2,3, and 7 to their highest power. That means the LCD is the number made from 2³ x 3 x 7 = 168.


if you have denominators of 50, 54, and 60, list their prime factors.

50 = 2 x 5²
54 = 2 x 3³
60 = 2² x 3 x 5

The LCD needs 2, 3, and 5, each to its highest power. This makes the LCD 2² x 3³ x 5² or 2700.

If you want the LCM of 75xy³ and 135x²y, factor everything into primes:

75xy³ = 3*5²*x*y³
135x²y = 3³*5*x²*y

The LCD needs 3, 5, x, and y each to its highest power. This makes the LCD 3³ * 5² * x² * y³ or 27*25x²y³ or 675.x²y³.

I hope that helps!! :-)

Answer 2

The two denominators are 3g^2 and 2g^5. The LCD is the simplest term that both can divide into.

Both denominators have a g^2, but we need g^5 to take care of both g terms. And one denominator has a 3 while the other has a 2, so 6 is the smallest number that will divide both. So the smallest term that will divide both 3g^2 and 2g^5 is 6g^5.

To get the first fraction into terms of 6g^5, we have to multiply the top and bottom by 2g^3. This gives 2g^3 / 6g^5. For the second fraction, we need to multiply the top and bottom by 3. This gives 9 / 6g^5.

Answer 3

The denominators are 3g^2 and 2g^5.
As the coefficients 3 and 2 are both prime, the LCD of these is their product, 6.
The LCD of g^2 and g^5 is g^5. That's the highest power of g.
g^2 means g * g
and g^5 means g * g * g * g * g
Clearly the first divides into the second to give g * g * g or g^3.
Combining these results, the LCD for the fractions is 6g^5.

Dividing 3g^2 into 6g^5 gives 2g^(5 - 2) = 2g^3.
The numerator of 1/3g^2 should therefore be multiplied by 2g^3 to become 2g^3.
That makes the first fraction 2g^3 / 6g^5.

Dividing 2g^5 into 6g^5 gives 3.
The numerator of 3/2g^5 should be multiplied by 3 giving 9g^5.
That makes the second fraction 9g^5 / 6g^5.

Answer 4

take the 2, 3, and g^5 to get 6g^5 as an LCD