How to solve 3/x + 2/y = 19/20

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 3/x + 2/y = 19/20 | Equatix

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Question

$$\frac{3}{x}+\frac{2}{y}=\frac{19}{20}$$

Solve for x

$x=-\frac{60y}{40-19y}$
$y\neq 0\text{ and }y\neq \frac{40}{19}$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $20xy$, the least common multiple of $x,y,20$.

$$20y\times 3+20x\times 2=19xy$$

Multiply $20$ and $3$ to get $60$.

$$60y+20x\times 2=19xy$$

Multiply $20$ and $2$ to get $40$.

$$60y+40x=19xy$$

Subtract $19xy$ from both sides.

$$60y+40x-19xy=0$$

Subtract $60y$ from both sides. Anything subtracted from zero gives its negation.

$$40x-19xy=-60y$$

Combine all terms containing $x$.

$$\left(40-19y\right)x=-60y$$

Divide both sides by $40-19y$.

$$\frac{\left(40-19y\right)x}{40-19y}=-\frac{60y}{40-19y}$$

Dividing by $40-19y$ undoes the multiplication by $40-19y$.

$$x=-\frac{60y}{40-19y}$$

Variable $x$ cannot be equal to $0$.

$$x=-\frac{60y}{40-19y}\text{, }x\neq 0$$

Show Solution

Solve for y

$y=-\frac{40x}{60-19x}$
$x\neq 0\text{ and }x\neq \frac{60}{19}$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $20xy$, the least common multiple of $x,y,20$.

$$20y\times 3+20x\times 2=19xy$$

Multiply $20$ and $3$ to get $60$.

$$60y+20x\times 2=19xy$$

Multiply $20$ and $2$ to get $40$.

$$60y+40x=19xy$$

Subtract $19xy$ from both sides.

$$60y+40x-19xy=0$$

Subtract $40x$ from both sides. Anything subtracted from zero gives its negation.

$$60y-19xy=-40x$$

Combine all terms containing $y$.

$$\left(60-19x\right)y=-40x$$

Divide both sides by $60-19x$.

$$\frac{\left(60-19x\right)y}{60-19x}=-\frac{40x}{60-19x}$$

Dividing by $60-19x$ undoes the multiplication by $60-19x$.

$$y=-\frac{40x}{60-19x}$$

Variable $y$ cannot be equal to $0$.

$$y=-\frac{40x}{60-19x}\text{, }y\neq 0$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

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Example

Question

Solve for x

Steps for Solving Linear Equation

Solve for y

Steps for Solving Linear Equation