Can anyone answer this question which is in a form of a fraction?
Simplify:
8x^2+20x-12/8x^2-2
Thanks
What does this expression equal? What do you mean by the word "answer"? Did you mean to type
8x^2+20x-12/(8x^2-2)=0 ?
the answer is: 2(x+3)/2x+1
) In an election there were four candidates: Arjan, Bess, Colin and Diane.
Between 400-450 people voted.
Exactly 2/5 voted for Arjan, 1/3 for Bess and 1/4 for Colin.
a. How many people voted altogether?
b. How many voted for Diane?
5) I am thinking of two fractions.
When I add them, I get 8/15.
When I multiply them I get 1/24
To solve these problems, you can use algebraic techniques such as equations and fractions manipulation.
For problem 1:
To simplify the fraction (8x^2+20x-12) / (8x^2-2), you can factor both the numerator and the denominator if possible. In this case, both the numerator and the denominator can be factored.
The numerator can be factored as 4(2x^2+5x-3) and the denominator can be factored as 2(4x^2-1).
So, the fraction becomes [ 4(2x^2+5x-3) ] / [ 2(4x^2-1) ].
Next, you can look for common factors and simplify the expression further. In this case, the 2's cancel out and you are left with (2x^2+5x-3) / (4x^2-1).
Finally, if you notice that the numerator can be further factored as (2x-1)(x+3), and the denominator can be factored as (2x-1)(2x+1), you can cancel out the common factors:
(2x-1)(x+3) / [(2x-1)(2x+1)].
Canceling out the common factor (2x-1), you are left with (x+3) / (2x+1), which is the simplified form of the fraction.
In conclusion, the simplified form of the fraction (8x^2+20x-12) / (8x^2-2) is (x+3) / (2x+1).
For problem 2:
a. To find how many people voted altogether, you need to add up the fractions of votes for each candidate.
The fraction of votes for Arjan is 2/5, for Bess is 1/3, and for Colin is 1/4.
To find the common denominator, multiply the denominators together: 5 * 3 * 4 = 60.
Now convert the fractions to have a common denominator of 60:
Arjan's fraction becomes (2/5) * (12/12) = 24/60.
Bess's fraction becomes (1/3) * (20/20) = 20/60.
Colin's fraction becomes (1/4) * (15/15) = 15/60.
Add up the fractions: 24/60 + 20/60 + 15/60 = 59/60.
Therefore, the total number of people who voted is 59 out of the range 400-450.
b. To find the number of people who voted for Diane, subtract the total votes from the given range of voters:
Between 400-450 people voted, and we found that 59 people voted for the other candidates. Therefore, the number of people who voted for Diane is 400-59 = 341.
For problem 3:
Let's call the two fractions a/b and c/d.
Given that a/b + c/d = 8/15 and a/b * c/d = 1/24.
To solve this, we can set up a system of equations. Let's replace a/b with x and c/d with y:
Equation 1: x + y = 8/15
Equation 2: x * y = 1/24
We can solve this system of equations using substitution or elimination.
Let's solve using substitution:
From Equation 1, we can express y in terms of x: y = 8/15 - x.
Then, substitute this into Equation 2: x * (8/15 - x) = 1/24.
Now, simplify the equation: (8x - 15x^2)/15 = 1/24.
Multiply both sides by 15 to eliminate the denominators: 8x - 15x^2 = 15/24.
Rearrange the equation: 15x^2 - 8x + 15/24 = 0.
To solve this quadratic equation, you can either factor, complete the square, or use the quadratic formula. In this case, the equation doesn't factor easily, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a,
where a = 15, b = -8, and c = 15/24.
Plugging in the values, you get:
x = [-(-8) ± √((-8)^2 - 4(15)(15/24))] / (2*15)
= (8 ± √(64 - 900/8)) / 30
= (8 ± √(-64/8)) / 30
= (8 ± √(-8)) / 30
Since we have a negative value inside the square root, the solutions will be complex numbers. So, x is either (8 ± i√8) / 30.
Therefore, the fractions a/b and c/d that satisfy the given conditions are (8 ± i√8) / 30 and (8 ∓ i√8) / 30.