Hi, hope this helps you out. I understand how this can be confusing. Have a great day! :)
Answer:
[tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]
Step-by-step explanation:
1. Factor [tex]y^2 - 3y + 2[/tex]:
How-to:
After breaking the expression into groups, you're left with [tex](y^2 - y) + (-2y + 2)[/tex]. Factor out y from [tex]y^2 - y[/tex][tex]: y(y - 1)[/tex]. Factor out [tex]-2[/tex] from [tex]-2y + 2: -2(y - 1)[/tex] = [tex]y( y - 1) - 2(y - 1)[/tex]. Finally, factor out common terms (in your case, y -1 ) and you're left with: [tex](y - 1)(y - 2)[/tex] Now you have [tex]\frac{3}{(y - 1)(y - 2)} + \frac{7}{y^2 - 1}[/tex]
2. Find the least common multiple of [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex].
How-to:
Find an expression comprised of factors that appear in [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex]. You'll find [tex](y - 1)(y - 2)(y + 1)[/tex]. Adjust your fractions based on the LCM and you'll get [tex]\frac{3(y + 1)}{(y - 1)(y - 2)(y + 1)} + \frac{7 (y - 2)}{(y + 1)(y - 1)(y - 2)}[/tex]
3. Since the denominators are equal, combine the fractions above. You'll get [tex]\frac{3(y + 1) + 7(y - 2)}{(y - 1)(y - 2)(y + 1)}[/tex]
4. Expand [tex]\frac{3(y + 1) + 7(y - 2)[/tex] and you'll get [tex]10y - 11[/tex]. This is your new numerator.
Finally, your simplified operation is: [tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]
