Solve for a
a=\frac{1}{3\left(b+5\right)}
b\neq -5
Solve for b
b=-5+\frac{1}{3a}
a\neq 0
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3a\left(b+5\right)=1
Multiply both sides of the equation by b+5.
3ab+15a=1
Use the distributive property to multiply 3a by b+5.
\left(3b+15\right)a=1
Combine all terms containing a.
\frac{\left(3b+15\right)a}{3b+15}=\frac{1}{3b+15}
Divide both sides by 3b+15.
a=\frac{1}{3b+15}
Dividing by 3b+15 undoes the multiplication by 3b+15.
a=\frac{1}{3\left(b+5\right)}
Divide 1 by 3b+15.
3a\left(b+5\right)=1
Variable b cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by b+5.
3ab+15a=1
Use the distributive property to multiply 3a by b+5.
3ab=1-15a
Subtract 15a from both sides.
\frac{3ab}{3a}=\frac{1-15a}{3a}
Divide both sides by 3a.
b=\frac{1-15a}{3a}
Dividing by 3a undoes the multiplication by 3a.
b=-5+\frac{1}{3a}
Divide 1-15a by 3a.
b=-5+\frac{1}{3a}\text{, }b\neq -5
Variable b cannot be equal to -5.
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y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}