## DF001 one year ago Help with Algebra! (S-1/S)-(T+1/T)

1. DF001

$\frac{ S-1 }{ S} - \frac{ T+1 }{ T }$

2. DF001

The LCD is ST but, why can't ST be distributed to S-1 and T+1?

3. Hero

Multiply the first fraction by T/T and the 2nd fraction by s/s

4. DF001

But why not ST since ST is the LCD?

5. Hero

Try doing the step I just mentioned first. You might discover something In the process.

6. DF001

I figured it to be multiplied by t/t but, I was told to multiple the numerator and the denominator by the LCD..

7. DF001

the answer is 1t-1s/ts but, I just wanted to know if the LCD is ST then why is only T/T multiplied to the first fraction and S/S multiplied to the other

8. DF001

Are there exceptions or rules to this

9. Hero

If you do the work, you will discover Why for yourself.

10. DF001

I know how the work is done and I know how to find the LCD but, I don't know why cant I distribute the whole LCD

11. DF001

|dw:1442807209447:dw|

12. DF001

so LCD is ST but, I don't know why only the opposites are distributed to it's opposite fractions.. If I didn't know better, I would actually believe the wrong answer is right

13. Hero

Because you're simplifying expressions not solving equations. The appraches and processes involved with both are different. When solving equations, you're Usually solving for a variable such as x And When doing so, the priority is to isolate x. . But here, we're asked to Combine fractions, not solve for a variable.

14. Hero

I hope that helps to ease your mind about this . I know this information doesn't particularly thrill you. gm Sorry about that, but this is just the way it is. Hopefully you'll find a way to accept it and move on with your studies.

15. DF001

Ok in this next example, could you explain the process to me$\frac{ y-2 }{ y-4 } + \frac{ 2y ^{2}-15y+12 }{ y^2-16 }$

16. DF001

Don't be sorry, :/.

17. Hero

Multiply the first fraction by (y+4)/(y+4 )

18. mathstudent55

You are confusing two different types of problems. When you have an equation, you can multiply both sides by the same quantity. If you have an equation involving denominators, one method of solving the equation is to multiply both sides by the LCD. The reason you do that step is that it eliminates all denominators. The reason you can do that step is that since the LCD is a number or an expression, you are simply multiplying both sides of the equation by the same thing. When you are adding or subtracting fractions, you need a common denominator. Often the common denominator that is used is the LCD. In this case (addition or subtraction of fractions), there are no two sides of an equation that you can multiply by the same quantity, the LCD. You simply need to have the same denominator in both fractions. After you find the LCD, you multiply one fraction by what it needs to end up with the LCD, and you multiply the other fraction by what it needs to end up with the LCD. Then you can add or subtract the fractions. Your original problem in this post is the second case above.

19. mathstudent55

Example of equation where you can multiply by the LCD: |dw:1442808629432:dw|

20. mathstudent55

Example of addition of fractions where you need the LCD to add the fractions: |dw:1442808954197:dw|

21. mathstudent55

In your second question above, you are again just adding fractions. You need to find the LCD. The denominator of the left fraction is already prime (non-factorable). The denominator of the right fraction can be factored. The first step is to factor the right denominator. Then using the two factored denominators, find the LCD. Then multiply one of both fractions by the correct fractions, so both fractions have the common denominator. Then you can add the fractions.