Assignments

Solve the assignments below. You can do this either by trying to determine a common divisor or by cross-multiplication. Which of the two is used depends on the nature of the assignment.

1. Solve:

$x-1=\displaystyle\frac{1}{x}$

Solution

2. Solve:

$\displaystyle\frac{2(x-4)}{3}=\displaystyle\frac{x-1}{2}$

Solution

3. Solve:

$\displaystyle\frac{x-3}{x+3}=\displaystyle\frac{x-4}{x+4}$

Solution

4. Solve:

$\displaystyle\frac{1}{x}=\displaystyle\frac{x+2}{x+3}$

Solution

5. Solve:

$\displaystyle\frac{4-2x}{3}=-5-x$

Solution

6. Solve:

$\displaystyle\frac{1}{\ln(x)}=\displaystyle\frac{\ln(x)-2}{3}$

Solution

7. For which value(s) of $p$ does the following equation have two different solutions?

$\displaystyle\frac{2x+p}{x-1}=\displaystyle\frac{x}{x+1}$

Solution

8. Solve:

$\displaystyle\frac{x^2-1}{x}-\displaystyle\frac{x+1}{2}=0$

Solution

9. For which value(s) of $p$ does the following equation have no solutions:

$\displaystyle\frac{x+p}{x-1}=2x$

Solution

10. Given the hyperbola:

$H: y=\displaystyle\frac{1}{x}$

and the line:

$l: y=px+1$

For which value(s) of $p$ is the line tangent to the hyperbola?

Solution

Equations with fractions

Assignments

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