Question

I am doing multiples rational expressions, if the equation is 5/2x + 1/4 = 9/2x what is the LDC and can you further explain the LDC to me?

Answer 1

Answer:

The answer is x = 8.

Step-by-step explanation:

LCD is the least common denominator of fractions. LCD represents the smallest number that can be used as a common denominator for a particular set of fractions.

The given equation is $\frac{5}{2x} + \frac{1}{4} = \frac{9}{2x}$

Here we can take LCD as 4x because 4x is divisible by 2x as $\frac{4x}{2x} = 2$,  4x is divisible by 4 as $\frac{4x}{4} = 1$

therefore we can write

$\frac{5}{2x} + \frac{1}{4} = \frac{9}{2x} \hspace{0.2cm} \Rightarrow \hspace{0.2cm} \frac{10}{4x} + \frac{x}{4x} = \frac{18}{4x} \hspace{0.2cm} \Rightarrow \hspace{0.2cm} \frac{x + 10}{4x} = \frac{18}{4x}$

now we can eliminate the LCD from both sides of the equation and we get

x + 10 = 18    $\therefore$      x  = 18 - 10       $\therefore$    x = 8.