Solve 4a^2/3a-3bdiv2a/b-a*3x/a

$$\frac { 4 a ^ { 2 } } { 3 a - 3 b } \div \frac { 2 a } { b - a } \times \frac { 3 x } { a }$$

Evaluate

$$-2x$$

Short Solution Steps

Divide \frac{4a^{2}}{3a-3b} by \frac{2a}{b-a} by multiplying \frac{4a^{2}}{3a-3b} by the reciprocal of \frac{2a}{b-a}.

$$\frac{4a^{2}\left(b-a\right)}{\left(3a-3b\right)\times 2a}\times \frac{3x}{a}$$

Cancel out 2a in both numerator and denominator.

$$\frac{2a\left(-a+b\right)}{3a-3b}\times \frac{3x}{a}$$

Factor the expressions that are not already factored in \frac{2a\left(-a+b\right)}{3a-3b}.

$$\frac{2a\left(-a+b\right)}{3\left(a-b\right)}\times \frac{3x}{a}$$

Extract the negative sign in -a+b.

$$\frac{-2a\left(a-b\right)}{3\left(a-b\right)}\times \frac{3x}{a}$$

Cancel out a-b in both numerator and denominator.

$$\frac{-2a}{3}\times \frac{3x}{a}$$

Multiply \frac{-2a}{3} times \frac{3x}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2a\times 3x}{3a}$$

Cancel out 3a in both numerator and denominator.

$$-2x$$

Differentiate w.r.t. x

$$-2$$

Steps Using Definition of a Derivative

Divide \frac{4a^{2}}{3a-3b} by \frac{2a}{b-a} by multiplying \frac{4a^{2}}{3a-3b} by the reciprocal of \frac{2a}{b-a}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4a^{2}\left(b-a\right)}{\left(3a-3b\right)\times 2a}\times \frac{3x}{a})$$

Cancel out 2a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2a\left(-a+b\right)}{3a-3b}\times \frac{3x}{a})$$

Factor the expressions that are not already factored in \frac{2a\left(-a+b\right)}{3a-3b}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2a\left(-a+b\right)}{3\left(a-b\right)}\times \frac{3x}{a})$$

Extract the negative sign in -a+b.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2a\left(a-b\right)}{3\left(a-b\right)}\times \frac{3x}{a})$$

Cancel out a-b in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2a}{3}\times \frac{3x}{a})$$

Multiply \frac{-2a}{3} times \frac{3x}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2a\times 3x}{3a})$$

Cancel out 3a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x)$$

The derivative of ax^{n} is nax^{n-1}.

$$-2x^{1-1}$$

Subtract 1 from 1.

$$-2x^{0}$$

For any term t except 0, t^{0}=1.

$$-2$$