Solve [(5/6*16/13)div(25/7div31/4)]frac{225}{48}=frac{x}{y}

$$[ ( \frac { 5 } { 6 } \times 1 \frac { 6 } { 13 } ) \div ( 2 \frac { 5 } { 7 } \div 3 \frac { 1 } { 4 } ) ] \frac { 225 } { 48 } = \frac { x } { y }$$

Solve for x

$$x=\frac{875y}{128}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 48y, the least common multiple of 48,y.

$$\frac{1092}{19}y\times \frac{5}{6}\times \frac{1\times 13+6}{13}\times \frac{225}{48}=48x$$

Multiply \frac{1092}{19} and \frac{5}{6} to get \frac{910}{19}.

$$\frac{910}{19}y\times \frac{1\times 13+6}{13}\times \frac{225}{48}=48x$$

Multiply 1 and 13 to get 13.

$$\frac{910}{19}y\times \frac{13+6}{13}\times \frac{225}{48}=48x$$

Add 13 and 6 to get 19.

$$\frac{910}{19}y\times \frac{19}{13}\times \frac{225}{48}=48x$$

Multiply \frac{910}{19} and \frac{19}{13} to get 70.

$$70y\times \frac{225}{48}=48x$$

Reduce the fraction \frac{225}{48} to lowest terms by extracting and canceling out 3.

$$70y\times \frac{75}{16}=48x$$

Multiply 70 and \frac{75}{16} to get \frac{2625}{8}.

$$\frac{2625}{8}y=48x$$

Swap sides so that all variable terms are on the left hand side.

$$48x=\frac{2625}{8}y$$

The equation is in standard form.

$$48x=\frac{2625y}{8}$$

Divide both sides by 48.

$$\frac{48x}{48}=\frac{2625y}{8\times 48}$$

Dividing by 48 undoes the multiplication by 48.

$$x=\frac{2625y}{8\times 48}$$

Divide \frac{2625y}{8} by 48.

$$x=\frac{875y}{128}$$

Solve for y

$$y=\frac{128x}{875}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 48y, the least common multiple of 48,y.

$$\frac{1092}{19}y\times \frac{5}{6}\times \frac{1\times 13+6}{13}\times \frac{225}{48}=48x$$

Multiply \frac{1092}{19} and \frac{5}{6} to get \frac{910}{19}.

$$\frac{910}{19}y\times \frac{1\times 13+6}{13}\times \frac{225}{48}=48x$$

Multiply 1 and 13 to get 13.

$$\frac{910}{19}y\times \frac{13+6}{13}\times \frac{225}{48}=48x$$

Add 13 and 6 to get 19.

$$\frac{910}{19}y\times \frac{19}{13}\times \frac{225}{48}=48x$$

Multiply \frac{910}{19} and \frac{19}{13} to get 70.

$$70y\times \frac{225}{48}=48x$$

Reduce the fraction \frac{225}{48} to lowest terms by extracting and canceling out 3.

$$70y\times \frac{75}{16}=48x$$

Multiply 70 and \frac{75}{16} to get \frac{2625}{8}.

$$\frac{2625}{8}y=48x$$

Divide both sides of the equation by \frac{2625}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2625}{8}y}{\frac{2625}{8}}=\frac{48x}{\frac{2625}{8}}$$

Dividing by \frac{2625}{8} undoes the multiplication by \frac{2625}{8}.

$$y=\frac{48x}{\frac{2625}{8}}$$

Divide 48x by \frac{2625}{8} by multiplying 48x by the reciprocal of \frac{2625}{8}.

$$y=\frac{128x}{875}$$

Variable y cannot be equal to 0.

$$y=\frac{128x}{875}\text{, }y\neq 0$$