please help me to simplify this expression:
2/y^2-3y+2 + 7/y^2-1
Do you mean
2/(y^2-3y+2) + 7/(y^2-1) ?
1/(y-1) can be factored out of both terms. That leaves you with
[1/(y-1)][2/(y-2) + 7/(y+1)]
That is not much simpler, however.
You could create a common denominator with the second bracketed term, but that won't simplify it much, either.
Please take care when transcribing questions involving fractions. All numerators and denominators have implicit parentheses around them, so when put onto a single line, they are necessary. An omission will change the value of the expression.
For example:
1/4x+3 is not the same as 1/(4x+3) because without parentheses division is done before addition.
(x+5)over 6= 1- (x+5) over 7
(x+5)/6= 1- (X+5)/7
I know you have to get a CD of 42 but I can't get the write answer.
To simplify the given expression:
1. Start by factoring the denominators of both fractions.
The denominator of the first fraction can be factored as (y-2)(y-1).
The denominator of the second fraction can be factored as (y+1)(y-1).
2. Rewrite the expression using the factored denominators.
The expression becomes:
2/(y-2)(y-1) + 7/(y+1)(y-1)
3. Find the least common denominator (LCD) of the two fractions.
The LCD is (y-2)(y-1)(y+1), which contains all the factors from both denominators.
4. Rewrite the fractions with the LCD as the common denominator.
The first fraction becomes:
(2*(y+1))/[(y-2)(y-1)(y+1)]
The second fraction remains the same:
7/[(y+1)(y-1)]
5. Add the fractions.
Since the denominators are now the same, the numerators can be directly added.
The expression now becomes:
(2*(y+1) + 7)/[(y-2)(y-1)(y+1)]
6. Simplify the numerator.
Multiply 2 by (y+1) to get 2y + 2.
The expression becomes:
(2y + 2 + 7)/[(y-2)(y-1)(y+1)]
7. Combine like terms in the numerator.
Add 2y and 2 to get 2y + 9.
The final simplified expression is:
(2y + 9)/[(y-2)(y-1)(y+1)]
Therefore, the simplified expression is (2y + 9)/[(y-2)(y-1)(y+1)].