SOLUTION: A student was given the following problem: 4x^2 -9/4x^2 +12x + 9 divided by 6x -9 . He states his answer to the problem as 3(2x -3). Is he correct? If not, explain why. What would

Algebra.Com
Question 156570: A student was given the following problem: 4x^2 -9/4x^2 +12x + 9 divided by 6x -9 . He states his answer to the problem as 3(2x -3). Is he correct? If not, explain why. What would you suggest he do to solve the problem?

Found 2 solutions by Edwin McCravy, gonzo:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
÷

Write the  as 

÷

Invert the second fraction and change the division
to multiplication:

×

Now factor  as .
Factor  as 
Factor  as 

and replace the numerators and denominatore by
their factored forms:

×

Indicate the multiplication of numerators and denominators,
so that we have just one fraction:



Cancel the 's



Cancel the  in the top with one of the 
's in the bottom:



All that's left is 



or



You can leave it like that, or distribute
out the bottom:



Edwin
Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!
my solution looks a little different - here's why.................
4x^2 - 9 / 4x^2+12x+9 / 6x-9
=
4x^2-9 / (4x^2+12x+9 * 6x-9)
because a/b/c = (a/b) * (1/c) = a/(b*c)
factoring we get...............
(2x-3) * (2x+3) / ( (2x+3) * (2x+3) * 3 * (2x-3) )
dividing out like terms we get ................
1 / ( (2x+3) * 3 )
because one (2x-3) on top cancels out one (2x-3) on bottom and one (2x+3) on top cancels out one (2x+3) on bottom.
so the answer appears to be 1 divided by (2x+3)*3.





RELATED QUESTIONS

A student was given the following problem: 4x^2-9 ______ divided by 6x-9 4x^2+12x+9 (answered by eperette)
A student was given the following problem:(4x^2-9) * [(6x - 9) / (4x^2 + 12x + 9)] . He... (answered by stanbon)
A student was given the following problem: 4x^2-9 _______ divided by 6x-9... (answered by Mathtut)
a student was given the problem 4x^2-9 divided by 6x-9... (answered by jim_thompson5910)
(16x^2 - 9)/((16x^2 - 24x +9) divided by (8x+6) He states his answer to the problem as... (answered by alicealc)
My teacher gave this problem 4x^-9 ------ 4x^2+12x+9 divided by... (answered by jim_thompson5910)
A student was given the following problem: (9x^2 divided by 16 over 9y^2-24y+16)... (answered by stanbon)
Which is the polynomial with integer coefficients that has degree 3 with zeros 0, -2, and (answered by mccravyedwin)
A student was thinking of three consecutive numbers. He said that the sum of the first... (answered by richard1234)