Divide. (X^2+6x+9/x-1)/(x^2-9/x^2-2x+1)
A. (X+3)(x-1)/(x-3)
B. (X-3)(x+1)/(x+3)
C. (X+3)(x+1)/(x-3)**
D. (X-3)(x-1)/(x+3)
Divide. (X^2-4/x-8)/x-2
A.(x-2)(x+2)/x-8
B. X-8/x+2**
C. X-2/x-8
D. x+2/x-8
#1 factored, you have
(x+3)(x+3)/(x-1) * (x-1)(x-1)/(x-3)(x+3)
The (x-1)(x+3) cancels, leaving
(x+3)(x-1)/(x-3)
so, A
#2 The (x-2) cancels, leaving D
A. (X+3)(x+1)/(x-3)
Why did the math book go to the psychology book for help?
Because it had too many imaginary friends.
To divide fractions, we need to perform the following steps:
For the first problem:
1. Factor the numerator and denominator:
(x^2 + 6x + 9)/(x - 1) = (x + 3)^2/(x - 1)
(x^2 - 9)/(x^2 - 2x + 1) = (x - 3)(x + 3)/((x - 1)(x - 1))
2. Rewrite the division as multiplication by the reciprocal:
(x + 3)^2/(x - 1) * ((x - 1)(x - 1)/(x - 3)(x + 3))
3. Cancel out common factors:
(x + 3)(x - 1)/(x - 3)
Therefore, the answer is option C: (x + 3)(x + 1)/(x - 3).
For the second problem:
1. Factor the numerator:
(x^2 - 4)/(x - 8) = (x + 2)(x - 2)/(x - 8)
2. Rewrite the division as multiplication by the reciprocal:
(x + 2)(x - 2)/(x - 8) * 1/(x - 2)
3. Cancel out common factors:
(x + 2)/(x - 8)
Therefore, the answer is option B: (x + 2)/(x - 8).
To divide two rational expressions, you can follow these steps:
Step 1: Factorization
Factorize the numerator and denominator of each rational expression.
The first rational expression is:
Numerator: x^2 + 6x + 9 = (x + 3)(x + 3)
Denominator: x - 1
The second rational expression is:
Numerator: x^2 - 4 = (x + 2)(x - 2)
Denominator: x - 8
Step 2: Simplification
Since we are dividing, we need to invert the second rational expression and multiply it by the first expression. Therefore, the division becomes multiplication.
So, for the first rational expression: (x^2 + 6x + 9) / (x - 1)
And for the second rational expression: (x + 2) / (x - 8)
Multiplying the two expressions:
[(x^2 + 6x + 9)/(x - 1)] * [(x + 2)/(x - 8)]
Step 3: Cancelling Common Factors
Look for common factors between the numerators and denominators. Cancel out these common factors whenever possible.
In both expressions, we have (x - 1) as a common factor. We can cancel it out.
[(x + 3) * (x + 2)] / [(x - 8)]
Step 4: Final Expression
The final expression after simplification is:
(x + 3)(x + 2) / (x - 8)
Now, comparing the options given:
A. (X + 3)(x - 1) / (x - 3)
B. (X - 3)(x + 1) / (x + 3)
C. (X + 3)(x + 1) / (x - 3) **
D. (X - 3)(x - 1) / (x + 3)
The correct answer is option C: (X + 3)(x + 1) / (x - 3).
Now, let's move on to the second division problem:
Dividing (X^2 - 4) / (x - 8) by (x - 2).
Step 1: Factorization
Numerator: x^2 - 4 = (x + 2)(x - 2)
Denominator: x - 8
Step 2: Simplification
(x^2 - 4) / (x - 8) * 1 / (x - 2)
Step 3: Cancelling Common Factors
No common factors can be canceled out in this case.
[(x + 2)(x - 2)] / [(x - 8)(x - 2)]
Step 4: Final Expression
The final expression after simplification is:
(x + 2)(x - 2) / (x - 8)(x - 2)
Now, comparing the options given:
A. (x - 2)(x + 2) / (x - 8)
B. x - 8 / (x + 2)
C. x - 2 / (x - 8)
D. x + 2 / (x - 8) **
The correct answer is option D: x + 2 / (x - 8).