Question 677436
{{{(y+5)/(y-5) - (y-6)/(y-7) + (2)/(y^2-12y+35)}}}
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{{{(y+5)/(y-5) - (y-6)/(y-7) + (2)/((y-7)(y-5))}}}
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Create the common denominator
{{{((y+5)/(y-5))((y-7)/(y-7)) - ((y-6)/(y-7))((y-5)/(y-5)) + (2)/((y-7)(y-5))}}}
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{{{((y+5)(y-7))/((y-5)(y-7)) - ((y-6)(y-5))/((y-7)(y-5)) + (2)/((y-7)(y-5))}}}
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{{{((y+5)(y-7)-(y-6)(y-5)+2)/((y-7)(y-5))}}}
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Numerator
(y+5)(y-7) = {{{y^2-7y+5y-35}}} = {{{y^2-2y-35}}}
(y-6)(y-5) = {{{y^2-5y-6y+30}}} = {{{y^2-11y+30}}}
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{{{(y^2-2y-35)-(y^2-11y+30)+2}}}
Distribute the negative
{{{y^2 - 2y - 35 - y^2 + 11y - 30 + 2}}}
9y - 63
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{{{(9y-63)/((y-7)(y-5)) = 9(y-7)/((y-7)(y-5)) = highlight_green(9/(y-5))}}}
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