91Ó°ÊÓ

For the following problems, solve the rational equations. Solve \(I=\frac{E}{R+r}\) for \(r\)

For the following problems, convert the given rational expressions to rational expressions having the same denominators. $$ \frac{x-2}{2 x^{2}+5 x-3}, \frac{x-1}{5 x^{2}+16 x+3} $$

For the following problems, add or subtract the rational expressions. $$ \frac{2 y^{2}+11 y-1}{y+4}-3 y $$

For the following problems, find the solution. When the same number is subtracted from both terms of the fraction \(\frac{7}{12}\), the result is \(\frac{1}{2}\). What is the number?

For the following problems, find the solution. When the same number is added to both terms of the fraction \(\frac{13}{15}\), the result is \(\frac{8}{9}\). What is the number?

For the following problems, add or subtract the rational expressions. $$ \frac{5 y^{2}-2 y+1}{y^{2}+y-6}-2 $$

For the following problems, convert the given rational expressions to rational expressions having the same denominators. $$ \frac{2}{x-5}, \frac{-3}{5-x} $$

For the following problems, find the solution. When three fourths of a number is added to the reciprocal of the number, the result is \(\frac{173}{16}\). What is the number?

For the following problems, add or subtract the rational expressions. $$ \frac{4 a^{3}+2 a^{2}+a-1}{a^{2}+11 a+28}+3 a $$

For the following problems, find the solution. When one third of a number is added to the reciprocal of the number, the result is \(\frac{-127}{90} .\) What is the number?