# How do you simplify (3x)/(x^2+3x-10)- (2x)/(x^2+x-6)?

Sep 19, 2016

$\frac{x \left(x - 1\right)}{\left(x + 5\right) \left(x - 2\right) \left(x + 3\right)}$

#### Explanation:

Adding or subtracting of algebraic fractions is a part of Algebra which students find difficult to master. They are done in exactly the same way as arithmetic fractions.

$\rightarrow \text{find a common denomiator using factors}$
$\rightarrow \text{ make equivalent fractions}$
$\rightarrow \text{ simplify }$

FACTORISE FACTORISE FACTORISE FACTORISE!!!!!

$\frac{3 x}{{x}^{2} + 3 x - 10} - \frac{2 x}{{x}^{2} + 2 x - 6}$

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

The LCD must have each factor that is in each denominator, without duplicates.

(3xcolor(red)((x+3)) - 2xcolor(blue)((x+5)))/(color(blue)((x+5))(x-2)color(red)((x+3))

Each numerator is multiplied by the factor that is missing in its denominator .

Now simplify the numerator

$\frac{3 {x}^{2} + 9 x - 2 {x}^{2} - 10 x}{\left(x + 5\right) \left(x - 2\right) \left(x + 3\right)}$

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

=$\frac{x \left(x - 1\right)}{\left(x + 5\right) \left(x - 2\right) \left(x + 3\right)}$