+1904 Solve for a
\(\frac{a-1}{ab}=\frac{{1-a}^{-1}}{b}\)
\(\frac{a-1}{ab}=\frac{1-\frac{1}{{a}^{1}}}{b}\)
\(\frac{a-1}{ab}=\frac{1-\frac{1}{a}}{b}\)
\(\frac{a-1}{ab}\times b=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{b(a-1)}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{ab-1b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{ab-b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{ab}{ab}-\frac{b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(1-\frac{b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(1-\frac{1}{a}=\frac{1-\frac{1}{a}}{b}\times b\)
\(1-\frac{1}{a}=\frac{b(1-\frac{1}{a})}{b}\)
\(1-\frac{1}{a}=\frac{1b-\frac{1}{a}b}{b}\)
\(1-\frac{1}{a}=\frac{b-\frac{1}{a}b}{b}\)
\(1-\frac{1}{a}=\frac{b}{b}-\frac{\frac{1}{a}b}{b}\)
\(1-\frac{1}{a}=1-\frac{\frac{1}{a}b}{b}\)
\(1-\frac{1}{a}=1-\frac{1}{a}\)
\(1-\frac{1}{a}-1=1-\frac{1}{a}-1\)
\(\frac{1}{a}-0=1-\frac{1}{a}-1\)
\(\frac{1}{a}=1-\frac{1}{a}-1\)
\(\frac{1}{a}=\frac{1}{a}-0\)
\(\frac{1}{a}=\frac{1}{a}\)
\(\frac{1}{a}\times a=\frac{1}{a}\times a\)
\(\frac{a}{a}=\frac{1}{a}\times a\)
\(1=\frac{1}{a}\times a\)
\(1=\frac{1a}{a}\)
\(1=\frac{a}{a}\)
\(1=1\)
Becasue a disappears and you get a solution that is true, this means that a can be any number. It can be written as (-∞, ∞) or it can be written as {a|a is all real numbers}.
Solve for b
\(\frac{a-1}{ab}=\frac{{1-a}^{-1}}{b}\)
\(\frac{a-1}{ab}=\frac{1-\frac{1}{{a}^{1}}}{b}\)
\(\frac{a-1}{ab}=\frac{1-\frac{1}{a}}{b}\)
\(\frac{a-1}{ab}\times b=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{b(a-1)}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{ab-1b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{ab-b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)
\(\frac{ab-b}{ab}=\frac{b(1-\frac{1}{a})}{b}\)
\(\frac{ab-b}{ab}=1(1-\frac{1}{a})\)
\(\frac{ab-b}{ab}=1-\frac{1}{a}\)
\(\frac{ab-b}{ab}\times ab=(1-\frac{1}{a})\times ab\)
\(\frac{ab(ab-b)}{ab}=(1-\frac{1}{a})\times ab\)
\(1(ab-b)=(1-\frac{1}{a})\times ab\)
\(ab-b=(1-\frac{1}{a})\times ab\)
\(ab-b=ab(1-\frac{1}{a})\)
\(ab-b=1ab-\frac{1}{a}ab\)
\(ab-b=ab-\frac{1}{a}ab\)
\(ab-b=ab-\frac{1ab}{a}\)
\(ab-b=ab-\frac{ab}{a}\)
\(ab-b=ab-1b\)
\(ab-b=ab-b\)
\(ab-b+b=ab-b+b\)
\(ab+0b=ab-b+b\)
\(ab+0=ab-b+b\)
\(ab=ab-b+b\)
\(ab=ab+0b\)
\(ab=ab+0\)
\(ab=ab\)
\(\frac{ab}{a}=\frac{ab}{a}\)
\(b=\frac{ab}{b}\)
\(b=b\)
Because b is equal to b, b can be any number. It can be written as (-∞, ∞) or it can be written as {b|b is all real numbers}.
