Solve 4/a*b-4/a=1-a/a

$$\frac { 4 } { a \cdot b } - \frac { 4 } { a } = \frac { 1 - a } { a }$$

Solve for a

$$a=5-\frac{4}{b}$$

$$b\neq \frac{4}{5}\text{ and }b\neq 0$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of ab,a.

$$4-b\times 4=b\left(1-a\right)$$

Use the distributive property to multiply b by 1-a.

$$4-b\times 4=b-ba$$

Swap sides so that all variable terms are on the left hand side.

$$b-ba=4-b\times 4$$

Subtract b from both sides.

$$-ba=4-b\times 4-b$$

Multiply -1 and 4 to get -4.

$$-ba=4-4b-b$$

Combine -4b and -b to get -5b.

$$-ba=4-5b$$

The equation is in standard form.

$$\left(-b\right)a=4-5b$$

Divide both sides by -b.

$$\frac{\left(-b\right)a}{-b}=\frac{4-5b}{-b}$$

Dividing by -b undoes the multiplication by -b.

$$a=\frac{4-5b}{-b}$$

Divide 4-5b by -b.

$$a=5-\frac{4}{b}$$

Variable a cannot be equal to 0.

$$a=5-\frac{4}{b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{4}{a-5}$$

$$a\neq 5\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of ab,a.

$$4-b\times 4=b\left(1-a\right)$$

Use the distributive property to multiply b by 1-a.

$$4-b\times 4=b-ba$$

Subtract b from both sides.

$$4-b\times 4-b=-ba$$

Add ba to both sides.

$$4-b\times 4-b+ba=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-b\times 4-b+ba=-4$$

Multiply -1 and 4 to get -4.

$$-4b-b+ba=-4$$

Combine -4b and -b to get -5b.

$$-5b+ba=-4$$

Combine all terms containing b.

$$\left(-5+a\right)b=-4$$

The equation is in standard form.

$$\left(a-5\right)b=-4$$

Divide both sides by -5+a.

$$\frac{\left(a-5\right)b}{a-5}=-\frac{4}{a-5}$$

Dividing by -5+a undoes the multiplication by -5+a.

$$b=-\frac{4}{a-5}$$

Variable b cannot be equal to 0.

$$b=-\frac{4}{a-5}\text{, }b\neq 0$$