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.
- \( \frac{x^2-1}{ x+1}=\frac{x^2+(-1)}{ x+1}=\frac{x^2}{ x}+\frac{-1}{1}=x-1
\> \)
- \( (x+y)^2-(x-y)^2=x^2+y^2-x^2-y^2=0 \)
- \( \frac{9(x-4)^2}{3x-12}=\frac{3^2(x-4)2}{3x-12}=\frac{(3x-12)^2}{3x-12}
=3x-12 \)
- \( \frac{x^2y^5}{2x^{-3}}=x^2y^5\cdot2x^3=2x^6y^5 \)
- \( \frac{(2x^3+7x^2+6)-(2x^3-3x^2-17x+3)}{(x+8)+(x-8)}=\frac{(2x)^2-17x+9}{2x}
=2x-17x+9=-15x+9=-6x \)
- \( \frac{x^{-1}+y^{-1}}{
x^{-1}-y^{-1}}=\frac{(x+y)^{-1}}{(x-y)^{-1}}
=\left(\frac{x+y}{ x-y}\right)^{-1}=-\frac{x+y}{ x-y}=\frac{x+y}{
y-x} \)
Tags: t2,c1,A,V,algebra,factoring,non-calculus,rational-functions
I believe mathematically this is the same at
utf01-001. You may like these instructions better or worse than the other version.
– Eric Hsu 2008-07-14 16:23