If you spend a lot of evenings struggling with your math homework, online math homework help is for you. Get the answers you want as quickly as you want with free math homework help for school and college students. Math homework help online can be in the form of online calculators, solved examples with steps, tutorials and live discussion boards. With free homework help math will soon become one of your easiest subjects. Help on math homework has helped hundreds of students keep up with math classes and improve their grades.

## Help With Math Homework Online For Free

Free math homework help gives students the opportunity to learn from each other through discussion boards and public forums. Students can post their queries and get math homework help online from qualified tutors who post the answers and steps on how to solve problems. If you need help with math homework for free try the hundreds of math help websites and you can choose the ones you want to work with.

## Solved Examples

**Question 1:**Find the sum of $\frac{x + 2}{x + 3}$ and $\frac{x + 2}{x - 2}$

**Solution:**

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

= $\frac{x^2 - 4 + x^2 + 3x + 2x + 6}{(x + 3)(x - 2)}$

= $\frac{2x^2 + 5x + 2}{(x + 3)(x - 2)}$

=> $\frac{x + 2}{x + 3}$ + $\frac{x + 2}{x - 2}$ = $\frac{2x^2 + 5x + 2}{(x + 3)(x - 2)}$.

= $\frac{x^2 - 4 + x^2 + 3x + 2x + 6}{(x + 3)(x - 2)}$

= $\frac{2x^2 + 5x + 2}{(x + 3)(x - 2)}$

=> $\frac{x + 2}{x + 3}$ + $\frac{x + 2}{x - 2}$ = $\frac{2x^2 + 5x + 2}{(x + 3)(x - 2)}$.

**Question 2:**Write a rational expression whose numerator is a quadratic polynomial with zeros -5 and $\frac{2}{4}$ and whose denominator is a quadratic polynomial with zeros $\frac{1}{3}$ and -2.

**Solution:**

Numerator of rational expression = (x + 5)(x - $\frac{2}{4}$ )

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

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

= $\frac{1}{4}$ (4x

= $\frac{1}{4}$(4x

=> Numerator of rational expression = $\frac{1}{4}$(4x

Denominator of rational expression = (x + 2)(x - $\frac{1}{3}$)

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

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

= $\frac{1}{3}$ (3x

= $\frac{1}{3}$ (3x

=> Denominator of rational expression = $\frac{1}{3}$ (3x

=> Rational expression = $\frac{3(4x^2 + 18x - 10)}{4 (3x^2 + 5x - 2)}$.

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

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

= $\frac{1}{4}$ (4x

^{2}- 2x + 20x - 10)= $\frac{1}{4}$(4x

^{2}+ 18x - 10)=> Numerator of rational expression = $\frac{1}{4}$(4x

^{2}+ 18x - 10)Denominator of rational expression = (x + 2)(x - $\frac{1}{3}$)

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

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

= $\frac{1}{3}$ (3x

^{2}- x + 6x - 2)= $\frac{1}{3}$ (3x

^{2}+ 5x - 2)=> Denominator of rational expression = $\frac{1}{3}$ (3x

^{2}+ 5x - 2)=> Rational expression = $\frac{3(4x^2 + 18x - 10)}{4 (3x^2 + 5x - 2)}$.

**Question 3:**Express in lowest form, $\frac{2x^2 - x - 10}{2x^2 - 15x + 22}$.

**Solution:**

**Step 1:**

Factorized the polynomials

2x

^{2}- x - 10 = 2x

^{2}- 5x + 4x - 10

= x(2x - 5) + 2(2x - 5)

= (x + 2)(2x - 5)

=> 2x

^{2}- x - 10 = (x + 2)(2x - 5)

2x

^{2}- 15x + 22 = 2x

^{2}- 11x - 4x + 22

= x(2x - 11) - 2(2x - 11)

= (x - 2)(2x - 11)

=> 2x

^{2}- 15x + 22 = (x - 2)(2x - 11)

Step 2:

Step 2:

=> $\frac{2x^2 - x - 10}{2x^2 - 15x + 22}$ = $\frac{(x + 2)(2x - 5)}{(x - 2)(2x - 11)}$.