SOLUTION: HI, Please i need help with this, i dont understand how i am supposed to cancel terms to get the product. 2. Use the polynomial expressions to answer the question. F=

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Question 1182365: HI, Please i need help with this, i dont understand how i am supposed to cancel terms to get the product.

2. Use the polynomial expressions to answer the question.

F= +3x%2B2y+
G= +4x%5E2y+
H= +6x%5E2-5x%2B1+
J= +9x%5E2-4y%5E2+
K= +2xy+

The expression +G%2FH+
is multiplied with another rational expression, and the product is 2. What is the other rational expression?
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let the answer be in the form A%2FB
where A,B are two polynomial expressions
B is nonzero

The expression G%2FH multiplies with A%2FB to get the product of 2
%28G%2FH%29%2A%28A%2FB%29+=+2

Multiply both sides by H%2FG, which is the reciprocal of G%2FH, and that isolates A%2FB

So,
%28G%2FH%29%2A%28A%2FB%29+=+2

%28H%2FG%29%2A%28G%2FH%29%2A%28A%2FB%29+=+%28H%2FG%29%2A2

%28%28cross%28H%29%29%2FG%29%2A%28G%2F%28cross%28H%29%29%29%2A%28A%2FB%29+=+%28H%2FG%29%2A2

%281%2FG%29%2A%28G%2F1%29%2A%28A%2FB%29+=+%28H%2FG%29%2A2

%281%2F%28cross%28G%29%29%29%2A%28%28cross%28G%29%29%2F1%29%2A%28A%2FB%29+=+%28H%2FG%29%2A2

A%2FB+=+2%28H%2FG%29

Now apply substitution and do a bit of simplification
A%2FB+=+2%28H%2FG%29

A%2FB+=+%282H%29%2FG

A%2FB+=+%282%286x%5E2-5x%2B1%29%29%2F%284x%5E2y%29

A%2FB+=+%282%286x%5E2-5x%2B1%29%29%2F%282%2A2x%5E2y%29

A%2FB+=+%28highlight%282%29%286x%5E2-5x%2B1%29%29%2F%28highlight%282%29%2A2x%5E2y%29

A%2FB+=+%28cross%282%29%286x%5E2-5x%2B1%29%29%2F%28cross%282%29%2A2x%5E2y%29

A%2FB+=+%286x%5E2-5x%2B1%29%2F%282x%5E2y%29

Therefore, the other rational expression is %286x%5E2-5x%2B1%29%2F%282x%5E2y%29


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

HI, Please i need help with this, i dont understand how i am supposed to cancel terms to get the product.

2. Use the polynomial expressions to answer the question.

F= +3x%2B2y+
G= +4x%5E2y+
H= +6x%5E2-5x%2B1+
J= +9x%5E2-4y%5E2+
K= +2xy+

The expression +G%2FH+
is multiplied with another rational expression, and the product is 2. What is the other rational expression?
matrix%281%2C3%2C+G%2FH%2C+%22=%22%2C+4x%5E2y%2F%286x%5E2+-+5x+%2B+1%29%29 ====> 
With the denominator being 1, the numerator of the Number will be the same as the denominator since they will cancel each other out.
We then have: 
              
Now, 4x%5E2y needs to be multiplied by a polynomial to equal 2. To find this polynomial, we merely, DIVIDE 4x%5E2y by 2.
This results in matrix%281%2C3%2C+4x%5E2y%2F2%2C+%22=%22%2C+2x%5E2y%29

We finally get: 
This makes the rational expression, highlight%28highlight_green%28highlight%28%286x%5E2+-+5x+%2B+1%29%2F%282x%5E2y%29%29%29%29