simplify (8c+25)/(6c)+(5-2c)/(6c)

The original denominators must be nonzero:

c \neq 0

Let's simplify:

\frac{8 c + 25}{6 c} + \frac{5 - 2 c}{6 c}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{8 c + 25}{6 c} + \frac{5 - 2 c}{6 c}

\frac{(8 c + 25) \cdot 6 + (5 - 2 c) \cdot 6}{6 \cdot c \cdot 6}

\frac{(8 c + 25) \cdot 6 + (5 - 2 c) \cdot 6}{6 \cdot c \cdot 6}

ⅰ

6 \cdot 6

36

\frac{(8 c + 25) \cdot 6 + (5 - 2 c) \cdot 6}{36 c}

ⓘ A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{(8 c + 25) \cdot 6 + (5 - 2 c) \cdot 6}{36 c}

\frac{(8 c + 25) + (5 - 2 c)}{6 c}

\frac{(8 c + 25) + (5 - 2 c)}{6 c}

ⓘ The numerator and the denominator are computed before the division:

25 + 5

30

■Like terms are grouped by adding their coefficients:

8 c - 2 c

6 c

ⅰ

\frac{6 c + 30}{6 c}

\frac{6}{6} + \frac{30}{6 c}

\frac{6}{6} + \frac{30}{6 c}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

6

, their greatest common divisor:

\frac{6}{6}

1

■A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{30}{6 c}

\frac{5}{c}

1 + \frac{5}{c}

▶Simplified form:

\frac{5}{c} + 1