LCD Problem

[ammomyers]

Thanks Soroban...I think I figured out the word problem using your help, but I cannot figure out to solve it. I know you have to find the LCD, but I am stumped on what it would be (I am basically teaching myself here, online Math class!)

1/x + 1/ x+5 = 1/6

so, would the LCD be x+5 * 6 ?

 

[soroban]

Hello again, ammomyers!

\(\displaystyle \text{We have: }\;\frac{1}{x} + \frac{1}{x+5} \:=\:\frac{1}{6}\)


In this problem, the LCD is the product of the denominators.

. . \(\displaystyle LCD \:=\:6x(x+5)\)


Multiply through by the LCD:

. . \(\displaystyle 6x(x+5)\!\cdot\!\frac{1}{x} \,+\, 6x(x+5)\!\cdot\!\frac{1}{x+5} \;\;=\;\;6x(x+5)\!\cdot\!\frac{1}{6}\)

And reduce: .\(\displaystyle 6(x+5) + 6x \;=\;x(x+5)\)


Then we have: .\(\displaystyle x^2 - 7x - 30 \:=\:0\)

. . which factors: .\(\displaystyle (x - 10)(x+3)\)

. . and has roots: .\(\displaystyle x \:=\:10,\,-3\)


The answer is: .\(\displaystyle x \:=\:10\) (hours, days, whatever)

 

[ammomyers]

If you are not teaching Math, you should be!!!! I got the LCD, but I didn't follow through with the problem...I didn't put everything to one side of the equation, so I got stuck...but I got it now! At least I will know how to do these kinds of problem for the test!

Thanks again!!!