Solve b^2*(a/b)^2-ab*(a/b)-2*(a/b)^2=0

$$b ^ { 2 } \times ( \frac { a } { b } ) ^ { 2 } - a b \times ( \frac { a } { b } ) - 2 \times ( \frac { a } { b } ) ^ { 2 } = 0$$

Solve for a

$$a=0$$

$$b\neq 0$$

Steps by Finding Square Root

Multiply both sides of the equation by b.

$$b\left(b^{2}\times \left(\frac{a}{b}\right)^{2}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$b\left(b^{2}\times \frac{a^{2}}{b^{2}}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Express b^{2}\times \frac{a^{2}}{b^{2}} as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Cancel out b^{2} in both numerator and denominator.

$$b\left(a^{2}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Express a\times \frac{a}{b} as a single fraction.

$$b\left(a^{2}-\frac{aa}{b}b\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$b\left(a^{2}-\frac{aa}{b}b\right)-2\times \frac{a^{2}}{b^{2}}b=0$$

Express 2\times \frac{a^{2}}{b^{2}} as a single fraction.

$$b\left(a^{2}-\frac{aa}{b}b\right)-\frac{2a^{2}}{b^{2}}b=0$$

Express \frac{2a^{2}}{b^{2}}b as a single fraction.

$$b\left(a^{2}-\frac{aa}{b}b\right)-\frac{2a^{2}b}{b^{2}}=0$$

Cancel out b in both numerator and denominator.

$$b\left(a^{2}-\frac{aa}{b}b\right)-\frac{2a^{2}}{b}=0$$

Multiply a and a to get a^{2}.

$$b\left(a^{2}-\frac{a^{2}}{b}b\right)-\frac{2a^{2}}{b}=0$$

Express \frac{a^{2}}{b}b as a single fraction.

$$b\left(a^{2}-\frac{a^{2}b}{b}\right)-\frac{2a^{2}}{b}=0$$

Cancel out b in both numerator and denominator.

$$b\left(a^{2}-a^{2}\right)-\frac{2a^{2}}{b}=0$$

Combine a^{2} and -a^{2} to get 0.

$$b\times 0-\frac{2a^{2}}{b}=0$$

Anything times zero gives zero.

$$0-\frac{2a^{2}}{b}=0$$

Anything plus zero gives itself.

$$-\frac{2a^{2}}{b}=0$$

Multiply both sides of the equation by b.

$$-2a^{2}=0$$

Divide both sides by -2. Zero divided by any non-zero number gives zero.

$$a^{2}=0$$

Take the square root of both sides of the equation.

$$a=0 a=0$$

The equation is now solved. Solutions are the same.

$$a=0$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by b.

$$b\left(b^{2}\times \left(\frac{a}{b}\right)^{2}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$b\left(b^{2}\times \frac{a^{2}}{b^{2}}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Express b^{2}\times \frac{a^{2}}{b^{2}} as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Cancel out b^{2} in both numerator and denominator.

$$b\left(a^{2}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Express a\times \frac{a}{b} as a single fraction.

$$b\left(a^{2}-\frac{aa}{b}b\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$b\left(a^{2}-\frac{aa}{b}b\right)-2\times \frac{a^{2}}{b^{2}}b=0$$

Express 2\times \frac{a^{2}}{b^{2}} as a single fraction.

$$b\left(a^{2}-\frac{aa}{b}b\right)-\frac{2a^{2}}{b^{2}}b=0$$

Express \frac{2a^{2}}{b^{2}}b as a single fraction.

$$b\left(a^{2}-\frac{aa}{b}b\right)-\frac{2a^{2}b}{b^{2}}=0$$

Cancel out b in both numerator and denominator.

$$b\left(a^{2}-\frac{aa}{b}b\right)-\frac{2a^{2}}{b}=0$$

Multiply a and a to get a^{2}.

$$b\left(a^{2}-\frac{a^{2}}{b}b\right)-\frac{2a^{2}}{b}=0$$

Express \frac{a^{2}}{b}b as a single fraction.

$$b\left(a^{2}-\frac{a^{2}b}{b}\right)-\frac{2a^{2}}{b}=0$$

Cancel out b in both numerator and denominator.

$$b\left(a^{2}-a^{2}\right)-\frac{2a^{2}}{b}=0$$

Combine a^{2} and -a^{2} to get 0.

$$b\times 0-\frac{2a^{2}}{b}=0$$

Anything times zero gives zero.

$$0-\frac{2a^{2}}{b}=0$$

Anything plus zero gives itself.

$$-\frac{2a^{2}}{b}=0$$

Multiply both sides of the equation by b.

$$-2a^{2}=0$$

Divide both sides by -2. Zero divided by any non-zero number gives zero.

$$a^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$a=\frac{0±0}{2}$$

Divide 0 by 2.

$$a=0$$

Solve for b

$$b\neq 0$$

$$a=0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$b\left(b^{2}\times \left(\frac{a}{b}\right)^{2}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$b\left(b^{2}\times \frac{a^{2}}{b^{2}}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Express b^{2}\times \frac{a^{2}}{b^{2}} as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-ab\times \frac{a}{b}\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

Express a\times \frac{a}{b} as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{aa}{b}b\right)-2\times \left(\frac{a}{b}\right)^{2}b=0$$

To raise \frac{a}{b} to a power, raise both numerator and denominator to the power and then divide.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{aa}{b}b\right)-2\times \frac{a^{2}}{b^{2}}b=0$$

Express 2\times \frac{a^{2}}{b^{2}} as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{aa}{b}b\right)-\frac{2a^{2}}{b^{2}}b=0$$

Express \frac{2a^{2}}{b^{2}}b as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{aa}{b}b\right)-\frac{2a^{2}b}{b^{2}}=0$$

Multiply a and a to get a^{2}.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{a^{2}}{b}b\right)-\frac{2a^{2}b}{b^{2}}=0$$

Express \frac{a^{2}}{b}b as a single fraction.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{a^{2}b}{b}\right)-\frac{2a^{2}b}{b^{2}}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b^{2} and b is b^{2}. Multiply \frac{a^{2}b}{b} times \frac{b}{b}.

$$b\left(\frac{b^{2}a^{2}}{b^{2}}-\frac{a^{2}bb}{b^{2}}\right)-\frac{2a^{2}b}{b^{2}}=0$$

Since \frac{b^{2}a^{2}}{b^{2}} and \frac{a^{2}bb}{b^{2}} have the same denominator, subtract them by subtracting their numerators.

$$b\times \frac{b^{2}a^{2}-a^{2}bb}{b^{2}}-\frac{2a^{2}b}{b^{2}}=0$$

Do the multiplications in b^{2}a^{2}-a^{2}bb.

$$b\times \frac{b^{2}a^{2}-a^{2}b^{2}}{b^{2}}-\frac{2a^{2}b}{b^{2}}=0$$

Combine like terms in b^{2}a^{2}-a^{2}b^{2}.

$$b\times \frac{0}{b^{2}}-\frac{2a^{2}b}{b^{2}}=0$$

Express b\times \frac{0}{b^{2}} as a single fraction.

$$\frac{b\times 0}{b^{2}}-\frac{2a^{2}b}{b^{2}}=0$$

Since \frac{b\times 0}{b^{2}} and \frac{2a^{2}b}{b^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{b\times 0-2a^{2}b}{b^{2}}=0$$

Do the multiplications in b\times 0-2a^{2}b.

$$\frac{-2a^{2}b}{b^{2}}=0$$

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}.

$$-2a^{2}b=0$$

The equation is in standard form.

$$\left(-2a^{2}\right)b=0$$

Divide 0 by -2a^{2}.

$$b=0$$

Variable b cannot be equal to 0.

$$b\in \emptyset$$