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\frac{\left(10^{2}+19x\right)\times 9}{2x+2y}
Divide 10^{2}+19x by \frac{2x+2y}{9} by multiplying 10^{2}+19x by the reciprocal of \frac{2x+2y}{9}.
\frac{\left(100+19x\right)\times 9}{2x+2y}
Calculate 10 to the power of 2 and get 100.
\frac{900+171x}{2x+2y}
Use the distributive property to multiply 100+19x by 9.
\frac{\left(10^{2}+19x\right)\times 9}{2x+2y}
Divide 10^{2}+19x by \frac{2x+2y}{9} by multiplying 10^{2}+19x by the reciprocal of \frac{2x+2y}{9}.
\frac{\left(100+19x\right)\times 9}{2x+2y}
Calculate 10 to the power of 2 and get 100.
\frac{900+171x}{2x+2y}
Use the distributive property to multiply 100+19x by 9.