Solve for a
a=2-\frac{3}{x}
x\neq 0\text{ and }x\neq 3
Solve for x
x=-\frac{3}{a-2}
a\neq 1\text{ and }a\neq 2
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ax=\left(x-3\right)\times 2+3
Multiply both sides of the equation by x-3, the least common multiple of x-3,3-x.
ax=2x-6+3
Use the distributive property to multiply x-3 by 2.
ax=2x-3
Add -6 and 3 to get -3.
xa=2x-3
The equation is in standard form.
\frac{xa}{x}=\frac{2x-3}{x}
Divide both sides by x.
a=\frac{2x-3}{x}
Dividing by x undoes the multiplication by x.
a=2-\frac{3}{x}
Divide 2x-3 by x.
ax=\left(x-3\right)\times 2+3
Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3, the least common multiple of x-3,3-x.
ax=2x-6+3
Use the distributive property to multiply x-3 by 2.
ax=2x-3
Add -6 and 3 to get -3.
ax-2x=-3
Subtract 2x from both sides.
\left(a-2\right)x=-3
Combine all terms containing x.
\frac{\left(a-2\right)x}{a-2}=-\frac{3}{a-2}
Divide both sides by -2+a.
x=-\frac{3}{a-2}
Dividing by -2+a undoes the multiplication by -2+a.
x=-\frac{3}{a-2}\text{, }x\neq 3
Variable x cannot be equal to 3.
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