Question

Resolva as equações literais, sendo X a icognita:

a). x/a-b = 2 - x/a+b

b). ax/b = 1/b + bx-1/a

Answer 1

$a)\frac{x}{a-b} = 2 - \frac{x}{a+b}\\ \\\frac{x}{a-b}+ \frac{x}{a+b} = 2\\ \\x\cdot\Big[ \frac{1}{a-b}+ \frac{1}{a+b} \Big]=2\\ \\x\cdot\Big[ \frac{a+b}{(a+b)\cdot(a-b)}+ \frac{a-b}{(a+b)\cdot(a-b)} \Big]=2\\ \\x\cdot\Big[ \frac{a+b+a-b}{a^2-b^2} \Big]=2\\  \\x\cdot\Big[ \frac{2a}{a^2-b^2} \Big]=2\\ \\x=\Big[ \frac{a^2-b^2}{2a} \Big]\cdot2\\ \\x= \frac{a^2-b^2}{a}$

$b)\frac{ax}{b} = \frac{1}{b}+\frac{bx-1}{a}\\ \frac{ax}{b} = \frac{1}{b}+\frac{bx}{a}-\frac{1}{a}\\ \frac{ax}{b}- \frac{bx}{a}= \frac{1}{b}-\frac{1}{a}\\ x\cdot\Big(\frac{a}{b}- \frac{b}{a}\Big)= \frac{a}{ab}-\frac{b}{ab}\\ x\cdot\Big(\frac{a^2}{ab}- \frac{b^2}{ab}\Big)= \frac{a-b}{ab}\\ x\cdot\Big(\frac{a^2-b^2}{ab}\Big)= \frac{a-b}{ab}\\ x=\frac{ab}{a^2-b^2} \cdot\frac{a-b}{ab}\\ x=\frac{ab}{(a+b)\cdot(a-b)} \cdot\frac{a-b}{ab}\\ x=\frac{1}{a+b}$