Many students spend long hours over math problems they don’t really understand, wondering how they’re supposed to solve it. Find online math solvers to make problem solving a lot easier and simpler. Math online helpers show you how to solve any math problem with all the steps. You will also find simple explanations which cover the theory behind the problem. Most online math solvers keep it simple so that students of all levels can understand and learn. Find out how to solve math problems easily and for free.

## How Do I Solve This Math Problem

Math online solvers will show you how to solve any math problem. Comprehensive and experienced, online math help is a great way to learn the subject on your own time and pace. There is no pressure to keep up with anyone since you are learning by yourself, one-on-one. Most websites have solved examples, which are a good reference on how to solve a math problem. Once you are clear on the concept, you can also make use of the large collection of worksheets available online to practice solving problems.

## Solved Examples

**Question 1:**Simplify $\frac{45x^{12}}{30x^6}$

**Solution:**

Given $\frac{45x^{12}}{30x^6}$

Step 1:

Factorized the numerator and denominator

45 x

30 x

Step 2:

$\frac{45x^{12}}{30x^6}$ = $\frac{3 * 3 * 5 * x^{12}}{ 2 * 3 * 5 * x^6}$

= $\frac{3 * x^{12}}{ 2 * x^6}$

= $\frac{3}{2}$$ x^{12 - 6}$

[ $\frac{x^m}{x^n}$ = x

= $\frac{3}{2}$$ x^6$

=> $\frac{45x^{12}}{30x^6}$ = $\frac{3}{2}$$ x^6$

Step 1:

Factorized the numerator and denominator

45 x

^{12}= 3 * 3 * 5 * x^{12}30 x

^{6}= 2 * 3 * 5 * x^{6}Step 2:

$\frac{45x^{12}}{30x^6}$ = $\frac{3 * 3 * 5 * x^{12}}{ 2 * 3 * 5 * x^6}$

= $\frac{3 * x^{12}}{ 2 * x^6}$

= $\frac{3}{2}$$ x^{12 - 6}$

[ $\frac{x^m}{x^n}$ = x

^{m - n}]= $\frac{3}{2}$$ x^6$

=> $\frac{45x^{12}}{30x^6}$ = $\frac{3}{2}$$ x^6$

**Question 2:**Solve the quadratic equation by using formula

2x

^{2}+ 5x - 3 = 0

**Solution:**

Given quadratic equation 2x

Comparing with equation ax

a = 2, b = 5 and c = - 3

b

= 25 + 24

= 49

and $\sqrt{b^2 - 4ac}$ = $\sqrt{49}$

= 7

=> $\sqrt{b^2 - 4ac}$ = 7

therefore

x = $\frac{- b \pm \sqrt{b^2 - 4ac}}{2a}$

= $\frac{- 5 \pm 7}{2 * 2}$

= $\frac{- 5 \pm 7}{4}$

=> x = $\frac{- 5 + 7}{4}$ or x = $\frac{- 5 - 7}{4}$

=> x = $\frac{1}{2}$, - 3.

^{2}+ 5x - 3 = 0Comparing with equation ax

^{2}+ bx + c = 0a = 2, b = 5 and c = - 3

b

^{2}- 4ac = 5^{2}- 4 * 2 * - 3= 25 + 24

= 49

and $\sqrt{b^2 - 4ac}$ = $\sqrt{49}$

= 7

=> $\sqrt{b^2 - 4ac}$ = 7

therefore

x = $\frac{- b \pm \sqrt{b^2 - 4ac}}{2a}$

= $\frac{- 5 \pm 7}{2 * 2}$

= $\frac{- 5 \pm 7}{4}$

=> x = $\frac{- 5 + 7}{4}$ or x = $\frac{- 5 - 7}{4}$

=> x = $\frac{1}{2}$, - 3.

**Question 3:**Simplify $\frac{x^3 - 2^3}{x^2 + 2x - 8}$

**Solution:**

Given, $\frac{x^3 - 2^3}{x^2 + 2x - 8}$

Step 1:

x

= (x - 2)(x

[x

and

x

= x(x + 4) - 2(x + 4)

= (x + 4)(x - 2)

Step 2:

$\frac{x^3 - 2^3}{x^2 + 2x - 8}$ = $\frac{ (x - 2)(x^2 + 2x + 4)}{ (x + 4)(x - 2) }$

= $\frac{x^2 + 2x + 4}{x + 4}$

=> $\frac{x^3 - 2^3}{x^2 + 2x - 8}$ = $\frac{x^2 + 2x + 4}{x + 4}$

Step 1:

x

^{3}- 2^{3}= (x - 2)(x^{2}+ 2x + 2^{2})= (x - 2)(x

^{2}+ 2x + 4)[x

^{3}- y^{3}= (x - y)(x^{2}+ xy + y^{2})]and

x

^{2}+ 2x - 8 = x^{2}+ 4x - 2x - 8= x(x + 4) - 2(x + 4)

= (x + 4)(x - 2)

Step 2:

$\frac{x^3 - 2^3}{x^2 + 2x - 8}$ = $\frac{ (x - 2)(x^2 + 2x + 4)}{ (x + 4)(x - 2) }$

= $\frac{x^2 + 2x + 4}{x + 4}$

=> $\frac{x^3 - 2^3}{x^2 + 2x - 8}$ = $\frac{x^2 + 2x + 4}{x + 4}$