Question 178228
3 over 2x-3 minus 5 over x = 1
{{{3/(2x-3) - 5/x = 1}}}
Start by multiplying both sides by a common denominator x(2x-3):
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{{{x(2x-3)(3/(2x-3) - 5/x) = x(2x-3)(1)}}}
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This results in:
{{{3x - 5(2x-3) = x(2x-3)}}}
{{{3x - 10x + 15 = 2x^2 - 3x }}}
{{{-7x + 15 = 2x^2 - 3x }}}
{{{15 = 2x^2 + 4x }}}
{{{0 = 2x^2 + 4x - 15}}}
Solve for 'x' using the quadratic equation yields:
x = {1.915, -3.915}
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Below are the details of the quadratic:
*[invoke quadratic "x", 2, 4, -15 ]