Simplifying

Simplifying can refer to:

• Reducing a fraction.
• Reducing the number of terms.
• Reducing the number of factors.

Example of reducing the number of terms

Simplify:
$ 1*x + 3 - 4*x + 8 $

Add terms.
=$ 5*x + 11 $

Example of reducing the number of factors

Simplify:
$ 2*3*7*x $

Multiply factors.
=$ 42*x $

Example of multiple forms of simplification

Simplify:
$ \frac{12*7*x-4*x}{3*2*x+5*x+9*x} $

Multiply factors.
=$ \frac{84*x-4*x}{6*x+5*x+9*x} $

Add terms.
=$ \frac{80*x}{20*x} $

Write the numerator and denominator as products of their prime factors:
=$ \frac{2*2*2*2*5*x}{2*2*5*x} $

The common factors are 2, 2, 5 and x. Divide numerator and denominator by 2*2*5*x:
= $ \frac{2*2*x}{1} $ = $ {2*2*x} $

Multiply factors.
=$ 4*x $

Example of Simplifying Algebraic Expressions

-2(x-9)/6 + 9(b-x-y)/7

-2x+18/6 + 9b-9x-9y/7

-2x + 18 + 9b - 9x - 9y/42

-11x+18+9b-9y/42