Finding the LCD of two expressions

[zolton5971]

Another question for you? Find the least common denominator of 3/(2x-2) and x/(5x-5)

I came up with 10?

 

[Prove It]

Another question for you? Find the least common denominator of 3/(2x-2) and x/(5x-5)

I came up with 10?

How could you possibly get 10 when your denominators both have an x in them?

Notice $\displaystyle \begin{align*} 2x - 2 = 2(x - 1) \end{align*}$ and $\displaystyle \begin{align*} 5x - 5 = 5( x - 1) \end{align*}$. So both already have a factor of $\displaystyle \begin{align*} (x - 1) \end{align*}$, so now you're just left finding the LCM of 2 and 5...

 

[MarkFL]

Another question for you? Find the least common denominator of 3/(2x-2) and x/(5x-5)

I came up with 10?

We ask that new questions not be tagged onto existing threads, as this can cause a thread to become convoluted and hard to follow, plus a new thread is likely to draw more attention. :D

So, I moved the relevant posts to a new thread.

 

[SuperSonic4]

We ask that new questions not be tagged onto existing threads, as this can cause a thread to become convoluted and hard to follow, plus a new thread is likely to draw more attention. :D

So, I moved the relevant posts to a new thread.

You're answer should include an \(\displaystyle x\) somewhere

The lowest common multiple (LCM) is given by splitting each term into prime factors and multiplying by the highest power of each prime factor. For example to find the LCM of 10 and 15 (it's 30) you'd do

\(\displaystyle 10 = 2 \times 5 \text{ and }\ 15 = 3 \times 5\) so the LCM is given by \(\displaystyle 2 \times 3 \times 5 = 30\)

You can do the same with algebraic fractions but remember to treat any polynomials or variables as prime - after simplifying you have \(\displaystyle \dfrac{3}{2}(x-1)^{-1}\) and \(\displaystyle 5(x-1)^{-1}\)

Can you use the method above to find the LCD?

 

[CellCoree]

The least common denominator (LCD) of two expressions is the smallest number that both denominators can evenly divide into. In this case, the expressions are 3/(2x-2) and x/(5x-5). To find the LCD, we need to factor the denominators and determine the common factors. The denominator of the first expression can be factored as 2(x-1), while the denominator of the second expression can be factored as 5(x-1). The common factor is (x-1). Therefore, the LCD is 2*5*(x-1), which simplifies to 10(x-1). Your answer of 10 is correct.