Directions: Decide whether the statements are true or false by using partial fraction decomposition. If the statement is false, show the correct way to decompose the partial fraction.
3/x^2+x-2=-1/x+2+1/x-1
Your non use of parenthesis makes this problem undecipherable.
Well the way the problem was on my paper, it doesn't have parenthesis so I wasn't sure if I should add them, sorry.
(3)/(x^2)+(x-2)=(-1)/(x+2)+(1)/(x-1)
You don't get it ...
I think you meant this:
3/(x^2+x-2)=-1/x+2+1/x-1
factor the left side:
3/((x+2)(x-1))=A/(x+2) + B/(x-1)
Now to solve A and B
3/((x+2)(x-1))=(A(x-1)+B(X+2))/((x+2)(x-1))
now comparing numerators,
3=Ax-A+Bx+2
and from that, Ax+Bx=0, or A=-B
and -A+2=3 or A=-1, so B=1
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which measure correctly completes the statement.
1,127.5 milligrams = ? grams (1 point)
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a sunflower was 1.8 meters high one week ago. in 7 days it grew 12 centimeters. find the current height of the sunflower.
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lesson 13 geometry
Partial fractions
To determine whether the given statement is true or false using partial fraction decomposition, we need to decompose the rational expressions on both sides of the equation.
Let's start with the left side of the equation:
3/x^2 + x - 2
To decompose this expression, we first need to factor the denominator.
The denominator x^2 + x - 2 can be factored as (x + 2)(x - 1).
Now we can express the left side of the equation as partial fractions:
3/x^2 + x - 2 = A/(x + 2) + B/(x - 1),
where A and B are constants to be determined.
To find the values of A and B, we need to combine the right side of the equation into a single rational expression with the same denominator:
-1/(x + 2) + 1/(x - 1).
Now, let's find a common denominator and simplify the right side of the equation:
(-1(x - 1) + 1(x + 2))/((x + 2)(x - 1)).
Simplifying further:
(-x + 1 + x + 2)/((x + 2)(x - 1)) = 3/((x + 2)(x - 1)).
Comparing this with our partial fraction decomposition:
3/x^2 + x - 2 = A/(x + 2) + B/(x - 1),
we can see that the coefficients of the two decompositions match. Hence, the given statement is true.
The correct decomposition is:
3/x^2 + x - 2 = 3/(x + 2) + 3/(x - 1).