what is the quotient 5-x/x^2 3x-4 divided by x^2-2x-15/x^2 5x 4 in simplified form state any restrictions on the variable
A.) -1/(x+3), x ≠ -3, x ≠ -4, ≠ 5
B.) (-(x+1)/(x-1)(x+3)), x ≠ 1, x ≠ -1, x ≠ -3, x ≠ -4, x ≠ 5
C.) (-(x+1)/(x-1)(x+3)), x ≠ 1, x ≠ -3
D.) ((-1)/(x+3)), x ≠ -3
B.) (-(x+1)/(x-1)(x+3)), x ≠ 1, x ≠ -1, x ≠ -3, x ≠ -4, x ≠ 5
The original posting was full of typos, so how did you get that answer?
I made the assumption that the original expression was intended to be:
(5-x)/(x^2-3x+4) divided by (x^2-2x-15)/(x^2+5x+4)
To simplify this expression, we first need to factor the denominators:
(5-x)/(x-1)(x-4) divided by (x-5)(x+3)/(x+1)(x+4)
Next, we invert the second fraction and multiply:
(5-x)/(x-1)(x-4) times (x+1)(x+4)/(x-5)(x+3)
To simplify, we cancel out common factors:
-(x+1)/(x-1)(x+3), x ≠ 1, x ≠ -1, x ≠ -3, x ≠ -4, x ≠ 5
Therefore, the correct answer is B.
To simplify the given expression 5-x/x^2 divided by 3x-4 divided by x^2-2x-15/x^2 5x 4, we need to follow these steps:
Step 1: Simplify each fraction separately.
Step 2: Invert the second fraction and multiply it with the first fraction.
Step 3: Simplify the resulting fraction.
Now let's break it down step-by-step:
Step 1: Simplify each fraction separately:
The given expression is: (5 - x) / (x^2) / (3x - 4) / (x^2 - 2x - 15) / (x^2 + 5x + 4)
Breaking them down individually:
Fraction A: (5 - x) / (x^2)
Fraction B: (3x - 4) / (x^2 - 2x - 15)
Fraction C: (x^2 - 2x - 15) / (x^2 + 5x + 4)
Step 2: Invert the second fraction and multiply it with the first fraction:
To do this, we multiply Fraction A and the reciprocal of Fraction B:
Fraction A * 1/Fraction B
So the expression becomes: (5 - x) / (x^2) * (x^2 - 2x - 15) / (3x - 4)
Step 3: Simplify the resulting fraction:
Now let's simplify the expression obtained from the previous step:
From the numerator:
(5 - x) * (x^2 - 2x - 15) = x^3 - 2x^2 - 15x - 5x^2 + 10x + 75
Simplifying it further: x^3 - 7x^2 - 5x + 75
From the denominator:
x^2 * (3x - 4) = 3x^3 - 4x^2
So, the simplified fraction is: (x^3 - 7x^2 - 5x + 75) / (3x^3 - 4x^2)
Now, let's find any restrictions on the variable (x).
Restrictions:
- Since the denominator of Fraction B is (x^2 - 2x - 15), we exclude the values of x where this denominator equals zero:
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x = 5, x = -3
Therefore, the restrictions on the variable x are x ≠ 5 and x ≠ -3.
Combining the simplified form and the restrictions, the answer is:
B.) (-(x + 1) / [(x - 1)(x + 3)]), x ≠ 1, x ≠ -1, x ≠ -3, x ≠ -4, x ≠ 5