Solve for K l=(K+1)/k-(m+1)/m

Math
l=K+1k-m+1m
Rewrite the equation as K+1k-m+1m=l.
K+1k-m+1m=l
Simplify the left side.
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To write K+1k as a fraction with a common denominator, multiply by mm.
K+1k⋅mm-m+1m=l
To write -m+1m as a fraction with a common denominator, multiply by kk.
K+1k⋅mm-m+1m⋅kk=l
Write each expression with a common denominator of km, by multiplying each by an appropriate factor of 1.
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Combine.
(K+1)mkm-m+1m⋅kk=l
Combine.
(K+1)mkm-(m+1)kmk=l
Reorder the factors of mk.
(K+1)mkm-(m+1)kkm=l
(K+1)mkm-(m+1)kkm=l
Combine the numerators over the common denominator.
(K+1)m-(m+1)kkm=l
Simplify the numerator.
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Apply the distributive property.
Km+1m-(m+1)kkm=l
Multiply m by 1.
Km+m-(m+1)kkm=l
Apply the distributive property.
Km+m+(-m-1⋅1)kkm=l
Multiply -1 by 1.
Km+m+(-m-1)kkm=l
Apply the distributive property.
Km+m-mk-1kkm=l
Rewrite -1k as -k.
Km+m-mk-kkm=l
Km+m-mk-kkm=l
Km+m-mk-kkm=l
Multiply both sides of the equation by km.
Km+m-mk-k=l⋅(km)
Remove parentheses.
Km+m-mk-k=l⋅(km)
Remove parentheses.
Km+m-mk-k=lkm
Move all terms not containing K to the right side of the equation.
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Subtract m from both sides of the equation.
Km-mk-k=lkm-m
Add mk to both sides of the equation.
Km-k=lkm-m+mk
Add k to both sides of the equation.
Km=lkm-m+mk+k
Km=lkm-m+mk+k
Divide each term by m and simplify.
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Divide each term in Km=lkm-m+mk+k by m.
Kmm=lkmm+-mm+mkm+km
Cancel the common factor of m.
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Cancel the common factor.
Kmm=lkmm+-mm+mkm+km
Divide K by 1.
K=lkmm+-mm+mkm+km
K=lkmm+-mm+mkm+km
Simplify each term.
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Cancel the common factor of m.
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Cancel the common factor.
K=lkmm+-mm+mkm+km
Divide lk by 1.
K=lk+-mm+mkm+km
K=lk+-mm+mkm+km
Cancel the common factor of m.
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Cancel the common factor.
K=lk+-mm+mkm+km
Divide -1 by 1.
K=lk-1+mkm+km
K=lk-1+mkm+km
Cancel the common factor of m.
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Cancel the common factor.
K=lk-1+mkm+km
Divide k by 1.
K=lk-1+k+km
K=lk-1+k+km
K=lk-1+k+km
K=lk-1+k+km
Solve for K l=(K+1)/k-(m+1)/m

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