Question

can someone please show me the steps to solve? I Keep getting the wrong answer
1/a= (1/2a)- (6/a^2)

Answer 1

\[\frac{ 1 }{ a } = \frac{ 1 }{ 2a } - \frac{ 6 }{ a^{2} }\]
right?

Answer 2

\[\frac{ 1 }{ a } = \frac{1}{2a}-\frac{6}{a^2}\]\[\frac{1}{a}=\frac{a-12}{2a^2}\]\[2a^2=a^2-12a\]\[a^2+12a=0\] which means\[a=0\]or\[a+12=0\]\[a=-12\]

Answer 3

But we cannot let a=0 because that will invalidate the original equation. So\[a=-12\]

Answer 4

another way to do this problem is "clear the denominators"
notice what happens if you multiply the equation (both sides and *all* terms ) by a^2
\[ a^2 \cdot \frac{ 1 }{ a } = a^2 \cdot\frac{ 1 }{ 2a } - a^2 \cdot\frac{ 6 }{ a^{2} } \\
a= \frac{a}{2} -6
\]
now you could add -a/2 to both sides and solve for a
\[ \frac{a}{2} = -6 \\ 2\cdot \frac{a}{2} = 2 \cdot -6 \\ a= -12 \]

Answer 5

Thank you all! I finally get it.