Multiply. The quotient of the quantity x plus 2 over the quantity 5 times x minus 15 times the quantity 10 times x squared minus 25 times x minus 15
A. The quantity 2 times x plus 1 over 5 times the quantity x minus 3
B. The quantity 2 times x plus 1 times the quantity x minus 3, all over 5
C. The quantity 10 times x plus 5 times the quantity x plus 2
D. The quantity x plus 2 times the quantity 2 times x plus 1
The first step is to simplify the expression inside the quotient:
x + 2 / (5x - 15(10x^2 - 25x - 15))
x + 2 / (5x - 150x^2 + 375x + 225)
x + 2 / (-150x^2 + 380x + 225)
Now we multiply this expression by the other polynomial:
(x + 2 / (-150x^2 + 380x + 225)) * (2x + 1)
To simplify this product, we can factor the denominator:
(-2/15) * (x + 2) / (x - 3) * (2x + 1)
Therefore, the answer is (A) the quantity 2 times x plus 1 over 5 times the quantity x minus 3.
Divide. The quantity x squared minus 4 over the quantity x minus 8, all divided by the quantity x minus 2
A. The quantity x minus 2 times the quantity x plus 2 divided by the quantity x minus 8
B. The quantity x minus 8 over the quantity x plus 2
C. The quantity x minus 2 over the quantity x minus 8
D. The quantity x plus 2 over the quantity x minus 8
To divide by a fraction, we can multiply by its reciprocal. In this case, we want to divide by the quantity (x-2), so we can multiply by its reciprocal, (1 / (x-2)), to get:
(x^2 - 4) / (x - 8) * (1 / (x - 2))
To simplify this expression, we can factor the numerator:
((x + 2)(x - 2)) / (x - 8) * (1 / (x - 2))
Now we can cancel out the (x-2) factor in the numerator and denominator:
(x + 2) / (x - 8)
Therefore, the answer is (D) the quantity x plus 2 over the quantity x minus 8.
Divide. start fraction start fraction x squared plus 2 x plus 1 over x minus 2 end fraction over start fraction x squared minus 1 over x squared minus 4 end fraction end fraction
A. Start Fraction left-parenthesis lower x plus 1 right-parenthesis left-parenthesis lower x plus 2 right-parenthesis over lower x minus 1 End Fraction
B. Start Fraction left-parenthesis lower x minus 1 right-parenthesis left-parenthesis lower x minus 2 right-parenthesis over lower x plus 1 End Fraction
C. Start Fraction left-parenthesis lower x minus 1 right-parenthesis left-parenthesis lower x plus 2 right-parenthesis over lower x plus 1 End Fraction
D. Start Fraction left-parenthesis lower x plus 1 right-parenthesis left-parenthesis lower x minus 2 right-parenthesis over lower x minus 1 End Fraction
bot please answer
To divide fractions, we can multiply by the reciprocal of the second fraction and then simplify.
Start by inverting the second fraction and changing division to multiplication:
start fraction start fraction x squared plus 2 x plus 1 over x minus 2 end fraction * start fraction x squared minus 4 over x squared minus 1 end fraction^(-1)
Now, factor the difference of squares in the second fraction:
start fraction start fraction x squared plus 2 x plus 1 over x minus 2 end fraction * start fraction (x + 2)(x - 2) over (x - 1)(x + 1) end fraction
Next, factor the numerator of the first fraction:
start fraction ((x + 1)(x + 1)) / (x - 2) * ((x + 2)(x - 2)) / ((x - 1)(x + 1)) end fraction
We can cancel out the (x+1) and (x-2) factors in the numerator and denominator:
start fraction (x + 1) * (x + 2) / ((x - 1) * (x + 1)) end fraction
Now we can simplify by canceling out the (x+1) factor in the numerator and denominator:
start fraction (x + 2) / (x - 1) end fraction
Therefore, the answer is (A) start fraction left-parenthesis lower x plus 1 right-parenthesis left-parenthesis lower x plus 2 right-parenthesis over lower x minus 1 end fraction.
Divide. The quantity 24 times w to the tenth power plus 8 times w to the twelfth power, all divided by 4 times w to the fourth power
A. 6 times w to the sixth power plus 2 times w to the eighth power
B. 6 times w to the sixth power plus 8 times w to the twelfth power
C. 24 times w to the tenth power plus 2 times w to the eighth power
D. 6 times w to the tenth power plus 2 times w to the twelfth power
We can simplify the expression by factoring out a common factor of 4w^4 from both terms in the numerator:
(24w^10 + 8w^12) / (4w^4) = 8w^4(3w^6 + w^8) / (4w^4)
Now we can simplify by canceling out the common factor of 4w^4:
8w^4(3w^6 + w^8) / (4w^4) = 2(3w^6 + w^8)
Therefore, the answer is (C) 24 times w to the tenth power plus 2 times w to the eighth power.
Divide. The quantity negative 6 times m to the ninth power minus 6 times m to the eighth power minus 16 times m to the sixth power, all divided by 2 times m to the third power
A. Negative 3 times m to the ninth power minus 3 times m to the eighth minus 8 times m to the sixth power
B. Negative 3 times m to the sixth power minus 6 times m to the eighth power minus 16 times m cubed
C. Negative 3 times m to the sixth power minus 3 times m to the fifth power minus 8 times m cubed
D. Negative 3 times m to the sixth power minus 3 times m to the fifth power minus 16 times m cubed
We can simplify the expression by factoring out a common factor of -2m^3 from all terms in the numerator:
(-6m^9 - 6m^8 - 16m^6) / (2m^3) = -2m^3(3m^6 + 3m^5 + 8m^3) / (2m^3)
Now we can simplify by canceling out the common factor of 2m^3:
-2m^3(3m^6 + 3m^5 + 8m^3) / (2m^3) = -3m^6 - 3m^5 - 8m^3
Therefore, the answer is (C) negative 3 times m to the sixth power minus 3 times m to the fifth power minus 8 times m cubed.