l=K+1k-m+1m

Rewrite the equation as K+1k-m+1m=l.

K+1k-m+1m=l

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.

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.

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

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 in Km=lkm-m+mk+k by m.

Kmm=lkmm+-mm+mkm+km

Cancel the common factor of m.

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.

Cancel the common factor of m.

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.

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.

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