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(2)/(5x)+(1)/(6)=(3)/(10x)+(1)/(3)\r
\n" ); document.write( "\n" ); document.write( "Since (1)/(6) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (1)/(6) from both sides.
\n" ); document.write( "(2)/(5x)=-(1)/(6)+(3)/(10x)+(1)/(3)\r
\n" ); document.write( "\n" ); document.write( "Simplify the right-hand side of the equation.
\n" ); document.write( "(2)/(5x)=(5x+9)/(30x)\r
\n" ); document.write( "\n" ); document.write( "Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
\n" ); document.write( "2*30x=(5x+9)*5x\r
\n" ); document.write( "\n" ); document.write( "Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
\n" ); document.write( "(5x+9)*5x=2*30x\r
\n" ); document.write( "\n" ); document.write( "Multiply (5x+9) by 5x to get 5x(5x+9).
\n" ); document.write( "5x(5x+9)=2*30x\r
\n" ); document.write( "\n" ); document.write( "Multiply 2 by 30x to get 60x.
\n" ); document.write( "5x(5x+9)=60x\r
\n" ); document.write( "\n" ); document.write( "Multiply 5x by each term inside the parenthesis (5x+9).
\n" ); document.write( "(5x(5x)+5x(9))=60x\r
\n" ); document.write( "\n" ); document.write( "Complete the multiplication of 5x by each term inside the parenthesis.
\n" ); document.write( "(25x^(2)+45x)=60x\r
\n" ); document.write( "\n" ); document.write( "Remove the parenthesis around the expression 25x^(2)+45x.
\n" ); document.write( "25x^(2)+45x=60x\r
\n" ); document.write( "\n" ); document.write( "Since 60x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 60x from both sides.
\n" ); document.write( "25x^(2)+45x-60x=0\r
\n" ); document.write( "\n" ); document.write( "Since 45x and -60x are like terms, add -60x to 45x to get -15x.
\n" ); document.write( "25x^(2)-15x=0\r
\n" ); document.write( "\n" ); document.write( "Factor out the GCF of 5x from each term in the polynomial.
\n" ); document.write( "5x(5x)+5x(-3)=0\r
\n" ); document.write( "\n" ); document.write( "Factor out the GCF of 5x from 25x^(2)-15x.
\n" ); document.write( "5x(5x-3)=0\r
\n" ); document.write( "\n" ); document.write( "Set the single term factor on the left-hand side of the equation equal to 0.
\n" ); document.write( "5x=0\r
\n" ); document.write( "\n" ); document.write( "Divide each term in the equation by 5.
\n" ); document.write( "(5x)/(5)=(0)/(5)\r
\n" ); document.write( "\n" ); document.write( "Simplify the left-hand side of the equation by canceling the common terms.
\n" ); document.write( "x=(0)/(5)\r
\n" ); document.write( "\n" ); document.write( "0 divided by any number or variable is 0.
\n" ); document.write( "x=0\r
\n" ); document.write( "\n" ); document.write( "Set each of the factors of the left-hand side of the equation equal to 0.
\n" ); document.write( "5x-3=0\r
\n" ); document.write( "\n" ); document.write( "Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
\n" ); document.write( "5x=3\r
\n" ); document.write( "\n" ); document.write( "Divide each term in the equation by 5.
\n" ); document.write( "(5x)/(5)=(3)/(5)\r
\n" ); document.write( "\n" ); document.write( "Simplify the left-hand side of the equation by canceling the common terms.
\n" ); document.write( "x=(3)/(5)\r
\n" ); document.write( "\n" ); document.write( "The complete solution is the set of the individual solutions.
\n" ); document.write( "x=0,(3)/(5) \n" ); document.write( "