document.write( "Question 80588: 25: Solve for the variable in each equation below.
\n" ); document.write( "[x / (x + 3)] + [1 / (x - 1)] = [4 / (x2 + 2x - 3)]
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Algebra.Com's Answer #57799 by tutorcecilia(2152)\"\" \"About 
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[x / (x + 3)] + [1 / (x - 1)] = [4 / (x2 + 2x - 3)]
\n" ); document.write( "(x / (x + 3)] + [1 / (x - 1)] = [4 / (x+3)(x-1)] [factor as much as possible and wherever possible]
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\n" ); document.write( "(x / (x + 3)] + [1 / (x - 1)] = [4 / (x+3)(x-1)][find the GCF: (x+3)(x-1) ]\r
\n" ); document.write( "\n" ); document.write( "((x+3)(x-1)(x / (x + 3)] + [( (x+3)(x-1) (1 / (x - 1)] = [( (x+3)(x-1) (4 / (x+3)(x-1))] [multiply each term by the GCF and cancel wherever possible]
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\n" ); document.write( "x(x-1)+1(x+3)=4
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\n" ); document.write( "\"%28x%5E2-x%29%2Bx%2B3%29%29\"=4 [simplify]
\n" ); document.write( "\"%28x%5E2-x%2Bx%2B3-4%29%29\"=0 [set the equation equal to zero by subtracting (4) from both sides]
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\n" ); document.write( "\"%28x%5E2-x%2Bx-1%29%29\"=0 [combine like-terms]
\n" ); document.write( "\"%28x%5E2-1%29%29\"=0 [combine like-terms]\r
\n" ); document.write( "\n" ); document.write( "(x+1)(x-1)=0 [try to factor or simplify as much as possible]
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\n" ); document.write( "x+1=0 [set each factor equal to zero and solve for the x-term
\n" ); document.write( "x=-1
\n" ); document.write( "and x-1=0
\n" ); document.write( "x=1
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\n" ); document.write( "Check each value of x by plugging them back into the original equation.
\n" ); document.write( "[x / (x + 3)] + [1 / (x - 1)] = [4 / (x2 + 2x - 3)]
\n" ); document.write( "Let x=-1
\n" ); document.write( "[(-1) / (-1 + 3)] + [1 / (-1 - 1)] = [4 / ((-1)^2 + 2(-1) - 3)]
\n" ); document.write( "(-1/2)+(1/-2)=(4/-4)
\n" ); document.write( "(-2/2)=(-4/4)
\n" ); document.write( "-1=-1 [checks out]
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\n" ); document.write( "[x / (x + 3)] + [1 / (x - 1)] = [4 / (x2 + 2x - 3)] \r
\n" ); document.write( "\n" ); document.write( "Let x=1
\n" ); document.write( "[1 / (1 + 3)] + [1 / (1 - 1)] = [4 / ((1)^2 + 2(1) - 3)]
\n" ); document.write( "(1/4)+(1/0)=(4/0)\r
\n" ); document.write( "\n" ); document.write( "This (x=1)will not work because zero cannot be in the denumerator.
\n" ); document.write( "So, the only answer is x=-1\r
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