Subtracting Rational Expressions

[joannamartinez]

I have a question please. On problem: 8/y-1/3=5/y The ansswer is y=9. I am having a hard time in showing the steps in solving. Would this be correct: 8+1=8 and 3=y=4+5=9 so the answer is 9. Is this correct? I forgot how I did it! Thank you.

 

[masters]

I have a question please. On problem: 8/y-1/3=5/y The ansswer is y=9. I am having a hard time in showing the steps in solving. Would this be correct: 8+1=8 and 3=y=4+5=9 so the answer is 9. Is this correct? I forgot how I did it! Thank you.

Hi joannamartinez,

You need to find the common denominator over your 3 fractions and multiply each of them by that common denominator.

\(\displaystyle \frac{8}{y}-\frac{1}{3}=\frac{5}{y}\)

It should be clear that the LCD (Least Common Denominator) is 3y.

\(\displaystyle 3y\left(\frac{8}{y}\right)-3y\left(\frac{1}{3}\right)=3y\left(\frac{5}{y}\right)\)

\(\displaystyle 24-y=15\)

\(\displaystyle -y=-9\)

\(\displaystyle y=9\)

 

[joannamartinez]

Thak you so much for clarifying it for me. I knew the answer was right but I did not know exactly how to show the correct steps. Thank you so very much.

 

[Denis]

I have a question please. On problem: 8/y - 1/3 = 5/y

Or go this way:
8/y - 5/y = 1/3
3/y = 1/3
y = 9