Solve (2-12/4k+3)^2/4+(6k/4k+3)^2/3=

$$\frac { ( 2 - \frac { 12 } { 4 k + 3 } ) ^ { 2 } } { 4 } + \frac { ( \frac { 6 k } { 4 k + 3 } ) ^ { 2 } } { 3 } =$$

Evaluate

$$\frac{28k^{2}-24k+9}{\left(4k+3\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{4k+3}{4k+3}.

$$\frac{\left(\frac{2\left(4k+3\right)}{4k+3}-\frac{12}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Since \frac{2\left(4k+3\right)}{4k+3} and \frac{12}{4k+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{2\left(4k+3\right)-12}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Do the multiplications in 2\left(4k+3\right)-12.

$$\frac{\left(\frac{8k+6-12}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Combine like terms in 8k+6-12.

$$\frac{\left(\frac{8k-6}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

To raise \frac{8k-6}{4k+3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Express \frac{\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}}}{4} as a single fraction.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

To raise \frac{6k}{4k+3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{\frac{\left(6k\right)^{2}}{\left(4k+3\right)^{2}}}{3}$$

Express \frac{\frac{\left(6k\right)^{2}}{\left(4k+3\right)^{2}}}{3} as a single fraction.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{\left(6k\right)^{2}}{\left(4k+3\right)^{2}\times 3}$$

Expand \left(6k\right)^{2}.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{6^{2}k^{2}}{\left(4k+3\right)^{2}\times 3}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{36k^{2}}{\left(4k+3\right)^{2}\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{12k^{2}}{\left(4k+3\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(4k+3\right)^{2}\times 4 and \left(4k+3\right)^{2} is 4\left(4k+3\right)^{2}. Multiply \frac{12k^{2}}{\left(4k+3\right)^{2}} times \frac{4}{4}.

$$\frac{\left(8k-6\right)^{2}}{4\left(4k+3\right)^{2}}+\frac{4\times 12k^{2}}{4\left(4k+3\right)^{2}}$$

Since \frac{\left(8k-6\right)^{2}}{4\left(4k+3\right)^{2}} and \frac{4\times 12k^{2}}{4\left(4k+3\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(8k-6\right)^{2}+4\times 12k^{2}}{4\left(4k+3\right)^{2}}$$

Do the multiplications in \left(8k-6\right)^{2}+4\times 12k^{2}.

$$\frac{64k^{2}-96k+36+48k^{2}}{4\left(4k+3\right)^{2}}$$

Combine like terms in 64k^{2}-96k+36+48k^{2}.

$$\frac{112k^{2}-96k+36}{4\left(4k+3\right)^{2}}$$

Factor the expressions that are not already factored in \frac{112k^{2}-96k+36}{4\left(4k+3\right)^{2}}.

$$\frac{4\left(28k^{2}-24k+9\right)}{4\left(4k+3\right)^{2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{28k^{2}-24k+9}{\left(4k+3\right)^{2}}$$

Expand \left(4k+3\right)^{2}.

$$\frac{28k^{2}-24k+9}{16k^{2}+24k+9}$$

Expand

$$\frac{28k^{2}-24k+9}{\left(4k+3\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{4k+3}{4k+3}.

$$\frac{\left(\frac{2\left(4k+3\right)}{4k+3}-\frac{12}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Since \frac{2\left(4k+3\right)}{4k+3} and \frac{12}{4k+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{2\left(4k+3\right)-12}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Do the multiplications in 2\left(4k+3\right)-12.

$$\frac{\left(\frac{8k+6-12}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Combine like terms in 8k+6-12.

$$\frac{\left(\frac{8k-6}{4k+3}\right)^{2}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

To raise \frac{8k-6}{4k+3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}}}{4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

Express \frac{\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}}}{4} as a single fraction.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{\left(\frac{6k}{4k+3}\right)^{2}}{3}$$

To raise \frac{6k}{4k+3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{\frac{\left(6k\right)^{2}}{\left(4k+3\right)^{2}}}{3}$$

Express \frac{\frac{\left(6k\right)^{2}}{\left(4k+3\right)^{2}}}{3} as a single fraction.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{\left(6k\right)^{2}}{\left(4k+3\right)^{2}\times 3}$$

Expand \left(6k\right)^{2}.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{6^{2}k^{2}}{\left(4k+3\right)^{2}\times 3}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{36k^{2}}{\left(4k+3\right)^{2}\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\left(8k-6\right)^{2}}{\left(4k+3\right)^{2}\times 4}+\frac{12k^{2}}{\left(4k+3\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(4k+3\right)^{2}\times 4 and \left(4k+3\right)^{2} is 4\left(4k+3\right)^{2}. Multiply \frac{12k^{2}}{\left(4k+3\right)^{2}} times \frac{4}{4}.

$$\frac{\left(8k-6\right)^{2}}{4\left(4k+3\right)^{2}}+\frac{4\times 12k^{2}}{4\left(4k+3\right)^{2}}$$

Since \frac{\left(8k-6\right)^{2}}{4\left(4k+3\right)^{2}} and \frac{4\times 12k^{2}}{4\left(4k+3\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(8k-6\right)^{2}+4\times 12k^{2}}{4\left(4k+3\right)^{2}}$$

Do the multiplications in \left(8k-6\right)^{2}+4\times 12k^{2}.

$$\frac{64k^{2}-96k+36+48k^{2}}{4\left(4k+3\right)^{2}}$$

Combine like terms in 64k^{2}-96k+36+48k^{2}.

$$\frac{112k^{2}-96k+36}{4\left(4k+3\right)^{2}}$$

Factor the expressions that are not already factored in \frac{112k^{2}-96k+36}{4\left(4k+3\right)^{2}}.

$$\frac{4\left(28k^{2}-24k+9\right)}{4\left(4k+3\right)^{2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{28k^{2}-24k+9}{\left(4k+3\right)^{2}}$$

Expand \left(4k+3\right)^{2}.

$$\frac{28k^{2}-24k+9}{16k^{2}+24k+9}$$