A lot of students struggle with learning Math in school. They find the
idea of solving math problems tough. Math tutoring online takes care of
this by offering one-on-one help with an expert online tutor. Online
Math tutors work with students to solve any math problem and help
improve their concept understanding and grades. Students can study from
the comfort of home and solve simple and complex math problem quickly
and easily. Online math tutoring sites put students in touch with
experienced math problem solvers and allows them to get instant answers
to their problems. Online Math tutoring sites have solved examples, which are a good reference on how to solve math problems making the subject easy.

## Online Math Tutoring

## Solved Examples

**Question 1:**Simplify $\frac{x^2 - x - 2}{x^2 - 4x - 5}$

**Solution:**

Given, $\frac{x^2 - x - 2}{x^2 - 4x - 5}$

Find the factors of quadratic equations

x

= x(x - 2) + (x - 2)

= (x + 1)(x - 2)

and

x

= x(x - 5) + (x - 5)

= (x + 1)(x - 5)

=> $\frac{x^2 - x - 2}{x^2 - 4x - 5}$ = $\frac{(x + 1)(x - 2)}{(x + 1)(x - 5)}$

= $\frac{x - 2}{x - 5}$

=> $\frac{x^2 - x - 2}{x^2 - 4x - 5}$ = $\frac{x - 2}{x - 5}$

**Step 1:**Find the factors of quadratic equations

x

^{2}- x - 2 = x^{2 }- 2x + x - 2= x(x - 2) + (x - 2)

= (x + 1)(x - 2)

and

x

^{2}- 4x - 5 = x^{2}- 5x + x - 5= x(x - 5) + (x - 5)

= (x + 1)(x - 5)

**Step 2:**=> $\frac{x^2 - x - 2}{x^2 - 4x - 5}$ = $\frac{(x + 1)(x - 2)}{(x + 1)(x - 5)}$

= $\frac{x - 2}{x - 5}$

=> $\frac{x^2 - x - 2}{x^2 - 4x - 5}$ = $\frac{x - 2}{x - 5}$

**Question 2:**An amusement park is planning a circular ride for children. If the radius of the circle is 14 feet, what is the area.

**Solution:**

Given

Radius of the circle (r) = 14

Let the area of circle = A

=> A = $\frac{22}{7}$ * (14)

=> A = $\frac{22}{7}$ * 14 * 14

=> A = 616 square feet.

Hence, area of the circular field id 616 square feet.

Radius of the circle (r) = 14

Let the area of circle = A

^{}Use the formula, A = ∏ r^{2}, where ∏ = $\frac{22}{7}$=> A = $\frac{22}{7}$ * (14)

^{2}=> A = $\frac{22}{7}$ * 14 * 14

=> A = 616 square feet.

Hence, area of the circular field id 616 square feet.

**Question 3:**The sum of three rational numbers is 3. If two of the numbers are $\frac{-3}{10}$ and $\frac{5}{15}$. Find the third number.

**Solution:**

Sum of the three numbers = 3

Two of the numbers are $\frac{-3}{10}$ and $\frac{5}{15}$

Sum of two numbers

=> $\frac{-3}{10}$ + $\frac{5}{15}$ = $\frac{-9 + 10}{30}$

= $\frac{1}{30}$

To find the third number, subtract sum of two numbers form the 3

=> Third number = 3 - $\frac{1}{30}$

= $\frac{90 - 1}{30}$

= $\frac{89}{30}$

Hence the third number is $\frac{89}{30}$.

Two of the numbers are $\frac{-3}{10}$ and $\frac{5}{15}$

**Step 1:**Sum of two numbers

=> $\frac{-3}{10}$ + $\frac{5}{15}$ = $\frac{-9 + 10}{30}$

= $\frac{1}{30}$

Step 2:Step 2:

To find the third number, subtract sum of two numbers form the 3

=> Third number = 3 - $\frac{1}{30}$

= $\frac{90 - 1}{30}$

= $\frac{89}{30}$

Hence the third number is $\frac{89}{30}$.