Solve 7*5=a(r^5-1)/r-1

$$7 \cdot 5 = \frac { a ( r ^ { 5 } - 1 ) } { r - 1 }$$

Solve for a

$$a=\frac{35}{r^{4}+r^{3}+r^{2}+r+1}$$

$$r\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r-1.

$$7\times 5\left(r-1\right)=a\left(r^{5}-1\right)$$

Multiply 7 and 5 to get 35.

$$35\left(r-1\right)=a\left(r^{5}-1\right)$$

Use the distributive property to multiply 35 by r-1.

$$35r-35=a\left(r^{5}-1\right)$$

Use the distributive property to multiply a by r^{5}-1.

$$35r-35=ar^{5}-a$$

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

$$ar^{5}-a=35r-35$$

Combine all terms containing a.

$$\left(r^{5}-1\right)a=35r-35$$

Divide both sides by r^{5}-1.

$$\frac{\left(r^{5}-1\right)a}{r^{5}-1}=\frac{35r-35}{r^{5}-1}$$

Dividing by r^{5}-1 undoes the multiplication by r^{5}-1.

$$a=\frac{35r-35}{r^{5}-1}$$

Divide -35+35r by r^{5}-1.

$$a=\frac{35}{r^{4}+r^{3}+r^{2}+r+1}$$