# Live Online Math Help

Math seems like a tough prospect to students simply because they have no idea what all those symbols and seemingly random letters mean. Not everyone can keep up with the teacher in class and since leaning math out of a textbook is not really possible, this leaves a lot of frustrated students who are convinced that math is a difficult subject. It doesn't have to be that way if you use online, live math help which will help you improve your grades and learn to enjoy the subject. Eventually, with free online math help and live tutors you make sense of algebra, geometry, trigonometry and the rest of it. Work with online tutors everyday for a little while, and your math grades will soon take an upward curve.

## Live Math Help Online Free

Live online math help has several advantages. You can work from home at any time you want. Its safe, reliable and available any time you want. Most importantly you can work with tutors who teach you according to your learning style. So you can go as fast or as slow as you want. The focus in online, live math help is on getting each student to understand the concepts and steps, rather than just skimming through the curriculum.

## Solved Examples

Question 1: Find GCD of 125 - 5x2 and x2 + 3x - 10
Solution:
Step 1:
Factorized polynomials

125 - 5x2 = 5(25 - x2 )

= 5(52 - x2 )

= 5(5 - x)(5 + x)       [a2 - b2 = (a - b)(a + b)]

and
x2 + 3x - 10 = x2 + 5x - 2x  - 10

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

= (x - 2)(x + 5)

Step 2:
125 - 5x2  = 5(5 - x)(5 + x)

x2 + 3x - 10 = (x - 2)(x + 5)

=> The required GCD = x + 5. answer

Question 2: Express in lowest term

$\frac{x^3 - 27}{5x^2 - 13x - 6}$
Solution:
Step 1:
Factorized polynomials

x3 - 27 = x3 - 33

= (x - 3)(x2 + 3x + 9)

[a3 - b3 = (a - b)(a2 + ab + b2 )]

and
5x2 - 13x - 6 = 5x2 - 15x + 2x - 6

= 5x(x - 3) + 2(x - 3)

= (5x + 2)(x - 3)

Step 2:
$\frac{x^3 - 27}{5x^2 - 13x - 6}$ = $\frac{ (x - 3)(x^2 + 3x + 9)}{(5x + 2)(x - 3)}$

= $\frac{x^2 + 3x + 9}{5x + 2}$

=> $\frac{x^3 - 27}{5x^2 - 13x - 6}$ = $\frac{x^2 + 3x + 9}{5x + 2}$

Question 3: Two numbers are in the ratio 2:3. If 5 is subtracted from the numerator and 3 added to the denominator, the ratio becomes 1:3. Find the numbers.
Solution:
Step 1:
Let the fraction is $\frac{x}{y}$

=> $\frac{x}{y}$ = $\frac{2}{3}$                                   ......................(1)

also given, when 5 is subtracted from the numerator and 3 added to the denominator, the ratio becomes 1:3.

=> $\frac{x - 5}{y + 3}$ = $\frac{1}{3}$                       ........................(2)

Step 2:

(1) => x = $\frac{2}{3}$y                                          ............................(3)

and (2) => 3(x - 5) = y + 3

=> 3x - 15 = y + 3

=> 3x - y = 18                                                       ................................(4)

Step 3:

Put x = $\frac{2}{3}$y in equation (4)

=> 3 * $\frac{2}{3}$ y - y = 18

=> 2y - y = 18

=> y = 18, put in equation (3)

=> x = $\frac{2}{3}$ * 18

=> x = 12

Hence the numbers are 12 and 18.