# Simplifying

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Simplifying can refer to:

### Example of reducing the number of terms

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

=$5*x + 11$

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

=$\frac{80*x}{20*x}$

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