(m+1)/m=5 — step-by-step solution

1) Let's solve in

ℝ

\frac{m + 1}{m} = 5

We multiply both sides by

m

, nonzero for the fractions to be defined

\frac{m + 1}{m} \cdot m = 5 m

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{m + 1}{m} \cdot m

\frac{(m + 1) \cdot m}{m}

■The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor

m

\frac{(m + 1) \cdot m}{m}

m + 1

m + 1 = 5 m

ⓘ We gather the terms in

m

on the right and the other terms on the left

1 = 5 m - m

ⓘ Like terms are grouped by adding their coefficients:

5 m - m

4 m

1 = 4 m

ⓘ Both sides are divided by

4

Candidates, pending the domain check:

m = \frac{1}{4}

For the expression

\frac{m + 1}{m}

to exist, you must check:

m \neq 0

Domain constraints:

m \neq 0

▶Solution:

m = \frac{1}{4}

2) The numeric value of:

m = \frac{1}{4}

equals:

▷

m = 0.25