Subtraction of Rational Expressions

Q.

If $\frac{1}{5}$:$\frac{1}{x}$=$\frac{1}{x}$:$\frac{1}{1.25}$, then the value of $x$ is

1. 5

2. 2.5

3. 5.2

4. 2

Q. Simplify $\frac{5x-3}{x}-\frac{3x+2}{x}.$

1. $\frac{2x-5}{x}$
2. $\frac{2x+5}{x}$
3. $\frac{2x-5}{x^2}$
4. $\frac{2x+5}{x^2}$

Q. $\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x}$

1. $\frac{6}{x}$
2. $\frac{4}{x}$
3. $\frac{7x}{11}$
4. $\frac{1}{x}$

Q. $\text{If}A=x-\frac{1}{x},\text{find}(A-\frac{1}{A})$ .

1. $\frac{x^4+3x^2+1}{3x^3-2x}$
2. $\frac{x^2-x^2+1}{x^3-x}$
3. $\frac{x^4-3x^2+1}{x^3-x}$
4. None of the above

Q. Simplify $\frac{x}{x^2+3x-4}+\frac{4x}{x^2+7x+12}.$

1. $\frac{x(5x-1)}{(x-1)(x+3)(x+4)}$
2. $\frac{x(5x+1)}{(x-1)(x+3)(x+4)}$
3. $\frac{x(5x-1)}{(x+1)(x+3)(x+4)}$
4. $\frac{x(5x+1)}{(x+1)(x+3)(x+4)}$

Q. Simplify $\frac{3}{x^2}-\frac{2}{5x}.$

1. $\frac{15-2x}{5x^2}$
2. $\frac{15+2x}{5x^2}$
3. $\frac{15-2x}{5x}$
4. $\frac{15+2x}{5x}$