Solve 3/x+6+1/3y+1 | Microsoft Math Solver

Evaluate

Differentiate w.r.t. x

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Algebra

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\frac{3\left(3y+1\right)}{\left(x+6\right)\left(3y+1\right)}+\frac{x+6}{\left(x+6\right)\left(3y+1\right)}

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+6 and 3y+1 is \left(x+6\right)\left(3y+1\right). Multiply \frac{3}{x+6} times \frac{3y+1}{3y+1}. Multiply \frac{1}{3y+1} times \frac{x+6}{x+6}.

\frac{3\left(3y+1\right)+x+6}{\left(x+6\right)\left(3y+1\right)}

Since \frac{3\left(3y+1\right)}{\left(x+6\right)\left(3y+1\right)} and \frac{x+6}{\left(x+6\right)\left(3y+1\right)} have the same denominator, add them by adding their numerators.

\frac{9y+3+x+6}{\left(x+6\right)\left(3y+1\right)}

Do the multiplications in 3\left(3y+1\right)+x+6.

\frac{9y+9+x}{\left(x+6\right)\left(3y+1\right)}

Combine like terms in 9y+3+x+6.

\frac{9y+9+x}{3xy+x+18y+6}

Expand \left(x+6\right)\left(3y+1\right).