How do you simplify #4/(x-2)-3/(x+1)+2/(x^2-x-2)#?
We need the denominators to be the same. We can do that by multiplying through with various forms of the number 1:
By signing up, you agree to our Terms of Service and Privacy Policy
To simplify the expression 4/(x-2) - 3/(x+1) + 2/(x^2-x-2), we need to find a common denominator for all the fractions. The common denominator is (x-2)(x+1).
Multiplying the first fraction by (x+1)/(x+1), the second fraction by (x-2)/(x-2), and the third fraction by (x-2)(x+1)/(x-2)(x+1), we get:
(4(x+1))/((x-2)(x+1)) - (3(x-2))/((x-2)(x+1)) + (2(x-2)(x+1))/((x-2)(x+1))
Simplifying further, we have:
(4x + 4 - 3x + 6 + 2x^2 - 2x - 4)/(x^2 - 3x - 2)
Combining like terms, we get:
(2x^2 - 3x + 6)/(x^2 - 3x - 2)
This is the simplified form of the expression 4/(x-2) - 3/(x+1) + 2/(x^2-x-2).
By signing up, you agree to our Terms of Service and Privacy Policy
To simplify the expression ( \frac{4}{x-2} - \frac{3}{x+1} + \frac{2}{x^2 - x - 2} ), first, find a common denominator for all the fractions. Then, combine them into a single fraction.
The common denominator for the three fractions is ( (x-2)(x+1)(x-2) ).
Rewriting each fraction with the common denominator:
[ \frac{4(x+1)}{(x-2)(x+1)} - \frac{3(x-2)}{(x-2)(x+1)} + \frac{2}{(x-2)(x+1)} ]
Combining the fractions:
[ \frac{4(x+1) - 3(x-2) + 2}{(x-2)(x+1)} ]
[ \frac{4x + 4 - 3x + 6 + 2}{(x-2)(x+1)} ]
[ \frac{x + 12}{(x-2)(x+1)} ]
So, the simplified expression is ( \frac{x + 12}{(x-2)(x+1)} ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- If y varies inversely as x and the constant of variation is 30, what is y when x = 6?
- How do you add #\frac { 1} { 6x } + \frac { 4} { 7x }#?
- How do you solve the system of equations #3x + 7y = - 3# and #x + \frac { 7} { 4} y = - \frac { 2} { 3}#?
- How do you simplify #(12n^4)/(21n^6 )#?
- How do you solve #\frac{6}{a + 5} = \frac{1}{4}#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7