Math Problems Database: Search for: "mike01-001"

mike01-001
Below is a list of some ``simple'' algebra problems. Some of the solutions are correct and some of them are {wrong}! For each problem:

determine if the answer is correct;
determine if there are any mistakes made in solving the problem and list them ({note} that just because the answer is correct does not mean there are no mistakes);
if there are mistakes, redo the problem correctly; if there are no mistakes, devise {ANOTHER} correct method to solve the problem.
1. \( \frac{x^2-1}{ x+1}=\frac{x^2+(-1)}{ x+1}=\frac{x^2}{ x}+\frac{-1}{1}=x-1 \> \)
2. \( (x+y)^2-(x-y)^2=x^2+y^2-x^2-y^2=0 \)
3. \( \frac{9(x-4)^2}{3x-12}=\frac{3^2(x-4)2}{3x-12}=\frac{(3x-12)^2}{3x-12} =3x-12 \)
4. \( \frac{x^2y^5}{2x^{-3}}=x^2y^5\cdot2x^3=2x^6y^5 \)
5. \( \frac{(2x^3+7x^2+6)-(2x^3-3x^2-17x+3)}{(x+8)+(x-8)}=\frac{(2x)^2-17x+9}{2x} =2x-17x+9=-15x+9=-6x \)
6. \( \frac{x^{-1}+y^{-1}}{ x^{-1}-y^{-1}}=\frac{(x+y)^{-1}}{(x-y)^{-1}} =\left(\frac{x+y}{ x-y}\right)^{-1}=-\frac{x+y}{ x-y}=\frac{x+y}{ y-x} \)

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