Solve for k 1/3k+1/4k=1

$\frac{1}{3} k + \frac{1}{4} k = 1$

Simplify $\frac{1}{3} k + \frac{1}{4} k$ .

Simplify each term.

Combine $\frac{1}{3}$ and $k$ .

$\frac{k}{3} + \frac{1}{4} k = 1$

Combine $\frac{1}{4}$ and $k$ .

$\frac{k}{3} + \frac{k}{4} = 1$

To write $\frac{k}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{k}{3} \cdot \frac{4}{4} + \frac{k}{4} = 1$

To write $\frac{k}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{k}{3} \cdot \frac{4}{4} + \frac{k}{4} \cdot \frac{3}{3} = 1$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{k}{3}$ by $\frac{4}{4}$ .

$\frac{k \cdot 4}{3 \cdot 4} + \frac{k}{4} \cdot \frac{3}{3} = 1$

Multiply $3$ by $4$ .

$\frac{k \cdot 4}{12} + \frac{k}{4} \cdot \frac{3}{3} = 1$

Multiply $\frac{k}{4}$ by $\frac{3}{3}$ .

$\frac{k \cdot 4}{12} + \frac{k \cdot 3}{4 \cdot 3} = 1$

Multiply $4$ by $3$ .

$\frac{k \cdot 4}{12} + \frac{k \cdot 3}{12} = 1$

Combine the numerators over the common denominator.

$\frac{k \cdot 4 + k \cdot 3}{12} = 1$

Simplify the numerator.

Move $4$ to the left of $k$ .

$\frac{4 \cdot k + k \cdot 3}{12} = 1$

Move $3$ to the left of $k$ .

$\frac{4 k + 3 \cdot k}{12} = 1$

Add $4 k$ and $3 k$ .

$\frac{7 k}{12} = 1$

Multiply both sides of the equation by $\frac{12}{7}$ .

$\frac{12}{7} \cdot \frac{7 k}{12} = \frac{12}{7} \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{7} \cdot \frac{7 k}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{7} \cdot \frac{7 k}{12} = \frac{12}{7} \cdot 1$

Rewrite the expression.

$\frac{1}{7} (7 k) = \frac{12}{7} \cdot 1$

Cancel the common factor of $7$ .

Factor $7$ out of $7 k$ .

$\frac{1}{7} (7 (k)) = \frac{12}{7} \cdot 1$

Cancel the common factor.

$\frac{1}{7} (7 k) = \frac{12}{7} \cdot 1$

Rewrite the expression.

$k = \frac{12}{7} \cdot 1$

Simplify the right side.

Multiply $\frac{12}{7}$ by $1$ .

$k = \frac{12}{7}$

The result can be shown in multiple forms.

Exact Form:

$k = \frac{12}{7}$

Decimal Form:

$k = 1.\overline{714285}$

Mixed Number Form:

$k = 1 \frac{5}{7}$

Solve for k 1/3k+1/4k=1

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