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.
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
3 answers
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
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.