Question 125759
1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3
{{{((x^2-3x))/((5x^2))}}} * {{{((10x))/((x^2-4x+3))}}}
:
{{{(x(x-3))/((x))}}} * {{{((2))/((x-3)(x-1))}}}; canceled 5x into 10x
:
(x-3) * {{{((2))/((x-3)(x-1))}}}; canceled out x
:
{{{((2))/((x-1))}}}; canceled out (x-3)
:
:
Solve.
2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared + 2x
{{{5/x}}} - {{{((x-3))/((x+2))}}} = {{{22/((x^2+2x))}}}
:
{{{5/x}}} - {{{((x-3))/((x+2))}}} = {{{22/(x(x+2))}}}
:
Multiply equation by x(x+2)
x(x+2)*{{{5/x}}} - x(x+2)*{{{((x-3))/((x+2))}}} = x(x+2)*{{{22/(x(x+2))}}}
Cancel out the denominators and you have:
:
5(x+2) - x(x-3) = 22
:
5x + 10 - x^2 + 3x = 22; multiplied what's inside the brackets
:
5x + 3x - x^2 + 10 - 22 = 0
:
-x^2 + 8x - 12 = 0
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This is easier to factor if we change the signs, multiiply by -1
x^2 - 8x + 12 = 0
factors to:
(x-6)(x-2) = 0
x = +6
x = +2
:
:
You can check both solutions in the original equation to confirm they are correct.