Solve (b/25w-a/750)*R=a

$$( \frac { b } { 25 w } - \frac { a } { 750 } ) \times R = a$$

Solve for R

$$\left\{\begin{matrix}R=\frac{750aw}{30b-aw}\text{, }&b\neq \frac{aw}{30}\text{ and }w\neq 0\\R\in \mathrm{R}\text{, }&b=0\text{ and }a=0\text{ and }w\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 750w, the least common multiple of 25w,750.

$$\left(\frac{b}{25w}-\frac{a}{750}\right)R\times 750w=a\times 750w$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25w and 750 is 750w. Multiply \frac{b}{25w} times \frac{30}{30}. Multiply \frac{a}{750} times \frac{w}{w}.

$$\left(\frac{30b}{750w}-\frac{aw}{750w}\right)R\times 750w=a\times 750w$$

Since \frac{30b}{750w} and \frac{aw}{750w} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30b-aw}{750w}R\times 750w=a\times 750w$$

Express \frac{30b-aw}{750w}R as a single fraction.

$$\frac{\left(30b-aw\right)R}{750w}\times 750w=a\times 750w$$

Express \frac{\left(30b-aw\right)R}{750w}\times 750 as a single fraction.

$$\frac{\left(30b-aw\right)R\times 750}{750w}w=a\times 750w$$

Cancel out 750 in both numerator and denominator.

$$\frac{R\left(-aw+30b\right)}{w}w=a\times 750w$$

Express \frac{R\left(-aw+30b\right)}{w}w as a single fraction.

$$\frac{R\left(-aw+30b\right)w}{w}=a\times 750w$$

Cancel out w in both numerator and denominator.

$$R\left(-aw+30b\right)=a\times 750w$$

Use the distributive property to multiply R by -aw+30b.

$$-Raw+30Rb=a\times 750w$$

Combine all terms containing R.

$$\left(-aw+30b\right)R=a\times 750w$$

The equation is in standard form.

$$\left(30b-aw\right)R=750aw$$

Divide both sides by -aw+30b.

$$\frac{\left(30b-aw\right)R}{30b-aw}=\frac{750aw}{30b-aw}$$

Dividing by -aw+30b undoes the multiplication by -aw+30b.

$$R=\frac{750aw}{30b-aw}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{30Rb}{w\left(R+750\right)}\text{, }&R\neq -750\text{ and }w\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }R=-750\text{ and }w\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 750w, the least common multiple of 25w,750.

$$\left(\frac{b}{25w}-\frac{a}{750}\right)R\times 750w=a\times 750w$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25w and 750 is 750w. Multiply \frac{b}{25w} times \frac{30}{30}. Multiply \frac{a}{750} times \frac{w}{w}.

$$\left(\frac{30b}{750w}-\frac{aw}{750w}\right)R\times 750w=a\times 750w$$

Since \frac{30b}{750w} and \frac{aw}{750w} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30b-aw}{750w}R\times 750w=a\times 750w$$

Express \frac{30b-aw}{750w}R as a single fraction.

$$\frac{\left(30b-aw\right)R}{750w}\times 750w=a\times 750w$$

Express \frac{\left(30b-aw\right)R}{750w}\times 750 as a single fraction.

$$\frac{\left(30b-aw\right)R\times 750}{750w}w=a\times 750w$$

Cancel out 750 in both numerator and denominator.

$$\frac{R\left(-aw+30b\right)}{w}w=a\times 750w$$

Express \frac{R\left(-aw+30b\right)}{w}w as a single fraction.

$$\frac{R\left(-aw+30b\right)w}{w}=a\times 750w$$

Cancel out w in both numerator and denominator.

$$R\left(-aw+30b\right)=a\times 750w$$

Use the distributive property to multiply R by -aw+30b.

$$-Raw+30Rb=a\times 750w$$

Subtract a\times 750w from both sides.

$$-Raw+30Rb-a\times 750w=0$$

Multiply -1 and 750 to get -750.

$$-Raw+30Rb-750aw=0$$

Subtract 30Rb from both sides. Anything subtracted from zero gives its negation.

$$-Raw-750aw=-30Rb$$

Combine all terms containing a.

$$\left(-Rw-750w\right)a=-30Rb$$

Divide both sides by -Rw-750w.

$$\frac{\left(-Rw-750w\right)a}{-Rw-750w}=-\frac{30Rb}{-Rw-750w}$$

Dividing by -Rw-750w undoes the multiplication by -Rw-750w.

$$a=-\frac{30Rb}{-Rw-750w}$$

Divide -30Rb by -Rw-750w.

$$a=\frac{30Rb}{w\left(R+750\right)}$$