# Solve for a pv(1+at)=qr(1+as)

pv(1+at)=qr(1+as)
Simplify pv(1+at).
Apply the distributive property.
pv⋅1+pv(at)=qr(1+as)
Multiply p by 1.
pv+pvat=qr(1+as)
pv+pvat=qr(1+as)
Simplify qr(1+as).
Apply the distributive property.
pv+pvat=qr⋅1+qr(as)
Multiply q by 1.
pv+pvat=qr+qras
pv+pvat=qr+qras
Subtract qras from both sides of the equation.
pv+pvat-qras=qr
Subtract pv from both sides of the equation.
pvat-qras=qr-pv
Factor a out of pvat-qras.
Factor a out of pvat.
a(pvt)-qras=qr-pv
Factor a out of -qras.
a(pvt)+a(-qrs)=qr-pv
Factor a out of a(pvt)+a(-qrs).
a(pvt-qrs)=qr-pv
a(pvt-qrs)=qr-pv
Divide each term by pvt-qrs and simplify.
Divide each term in a(pvt-qrs)=qr-pv by pvt-qrs.
a(pvt-qrs)pvt-qrs=qrpvt-qrs+-pvpvt-qrs
Cancel the common factor of pvt-qrs.
Cancel the common factor.
a(pvt-qrs)pvt-qrs=qrpvt-qrs+-pvpvt-qrs
Divide a by 1.
a=qrpvt-qrs+-pvpvt-qrs
a=qrpvt-qrs+-pvpvt-qrs
Simplify qrpvt-qrs+-pvpvt-qrs.
Move the negative in front of the fraction.
a=qrpvt-qrs-pvpvt-qrs
Combine the numerators over the common denominator.
a=qr-pvpvt-qrs
a=qr-pvpvt-qrs
a=qr-pvpvt-qrs
Solve for a pv(1+at)=qr(1+as)

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