Perform the indicated operation
y/y-5+5/5-y
•algebra - MathMate, Tuesday, June 14, 2011 at 10:45am
I have made a guess and put on the minimum parentheses for the problem to make sense. Do not forget to enclose numerators and denominators with parentheses when transcribing expressions from a book or other sources.
(y-4)/(y-9) - (y+1)/(y+9) + (y-99)/(y^2-81)
using (y-9)(y+9)=y²-81
=(y-4)/(y-9) - (y+1)/(y+9) + (y-99)/((y+9)(y-9))
=((y-4)(y+9)-(y+1)(y-9)+(y-99))/((y+9)(y-9))
=(y²+5y-36 - (y²-8y-9) + (y-99))/((y+9)(y-9))
=(14y-126)/((y+9)(y-9))
=14(y-9)/((y+9)(y-9))
=14/(y+9)
I'm guessing you meant
y/(y-5)+5/(5-y)
= y/(y-5) - 5/(y-5)
= (y-5)/(y-5)
= 1
To perform the indicated operation, we need to simplify the given expression. Let's break it down step by step:
The expression is: y / (y - 5) + 5 / (5 - y)
To combine the fractions, we need a common denominator. In this case, the common denominator is (y - 5) * (5 - y) since the two denominators are each other's negatives.
The first fraction: y / (y - 5) needs to be multiplied by (5 - y) / (5 - y).
The second fraction: 5 / (5 - y) needs to be multiplied by (y - 5) / (y - 5).
Now, we can combine the numerators since the denominators are the same:
[(y * (5 - y)) + (5 * (y - 5))] / [(y - 5) * (5 - y)]
Expanding the brackets:
[(5y - y^2) + (5y - 25)] / [(y - 5) * (5 - y)]
Combining like terms in the numerator:
(10y - y^2 - 25) / [(y - 5) * (5 - y)]
Since (y - 5) * (5 - y) = -(y - 5) * (y - 5) = -(y - 5)^2, the simplified expression is:
(10y - y^2 - 25) / -(y - 5)^2