Multiply. start fraction x squared plus 8x plus 15 over x minus 4 end fraction times start fraction x squared minus 16 over 2x plus 6 end fraction
A. start fraction x superscript 4 baseline plus 8 x minus 1 over 3 x plus 2 end fraction
B. start fraction left parenthesis x plus 5 right parenthesis left parenthesis x plus 4 right parenthesis over 2 end fraction
C. start fraction left parenthesis x minus 5 right parenthesis left parenthesis x plus 4 right parenthesis over 2 end fraction
D. start fraction x superscript 4 baseline plus 8 x superscript 3 baseline minus x over 2 x superscript 3 baseline minus 24 end fraction
AAAaannndd the bot gets it wrong yet again!
all those annoying words! So much easier using real math.
(x^2+8x+15)/(x-4) * (x^2-16)/(2x+6)
= (x+3)(x+5)/(x-4) * (x-4)(x+4)/(2(x+3))
= (x+5)(x+4)/2
So, B
I apologize for the mistake in my previous response. Your solution and answer B are correct. Thank you for providing a clear and concise explanation.
To multiply the given expression, we can simplify and cancel out common terms where possible.
First, let's simplify each fraction separately:
The first fraction \( \frac{x^2+8x+15}{x-4} \) can be factored as \( \frac{(x+3)(x+5)}{x-4} \).
The second fraction \( \frac{x^2-16}{2x+6} \) can be factored as \( \frac{(x-4)(x+4)}{2(x+3)} \).
Now, we can multiply the fractions:
\( \frac{(x+3)(x+5)}{x-4} \times \frac{(x-4)(x+4)}{2(x+3)} \)
We can cancel out the terms \((x-4)\) and \((x+3)\) in the numerator and denominator:
\( \frac{(x+5)(x+4)}{2} \)
Expanding the numerator:
\( \frac{x^2+9x+20}{2} \)
Therefore, the answer is A. \( \frac{x^2+9x+20}{2} \)
Solution:
First, we need to factor the given expressions:
start fraction x squared plus 8x plus 15 over x minus 4 end fraction = start fraction left parenthesis x plus 5 right parenthesis left parenthesis x plus 3 right parenthesis over x minus 4 end fraction
start fraction x squared minus 16 over 2x plus 6 end fraction = start fraction left parenthesis x plus 4 right parenthesis left parenthesis x minus 4 right parenthesis over 2 left parenthesis x plus 3 right parenthesis end fraction
Now, we can simplify the multiplication as follows:
start fraction x squared plus 8x plus 15 over x minus 4 end fraction times start fraction x squared minus 16 over 2x plus 6 end fraction
= start fraction left parenthesis x plus 5 right parenthesis left parenthesis x plus 3 right parenthesis over x minus 4 end fraction times start fraction left parenthesis x + 4 right parenthesis left parenthesis x - 4 right parenthesis over 2 left parenthesis x + 3 right parenthesis end fraction
= start fraction left parenthesis x + 5 right parenthesis left parenthesis x + 3 right parenthesis left parenthesis x + 4 right parenthesis left parenthesis x - 4 right parenthesis over 2 left parenthesis x + 3 right parenthesis left parenthesis x - 4 right parenthesis end fraction
= start fraction x² + 8x - 1 over 2x + 3 end fraction
Hence, the answer is (A) start fraction x² + 8x - 1 over 2x + 3 end fraction.