log((12*x-2*sqrt(42))*1/(2*sqrt(42)+12*x))*1/(2*sqrt(42)) если x=3/2 (упростите выражение)

$$frac{1}{2 sqrt{42}} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$

$$frac{1}{2 sqrt{42}} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$

log((12*(3/2) – 2*sqrt(42))/(2*sqrt(42) + 12*(3/2)))/(2*sqrt(42))

$$frac{1}{2 sqrt{42}} log{left (frac{12 (3/2) – 2 sqrt{42}}{12 (3/2) + 2 sqrt{42}} right )}$$

log((12*3/2 – 2*sqrt(42))/(2*sqrt(42) + 12*3/2))/(2*sqrt(42))

$$frac{1}{2 sqrt{42}} log{left (frac{- 2 sqrt{42} + frac{36}{2}}{2 sqrt{42} + frac{36}{2}} right )}$$

sqrt(42)*log((18 – 2*sqrt(42))/(18 + 2*sqrt(42)))/84

$$frac{sqrt{42}}{84} log{left (frac{- 2 sqrt{42} + 18}{2 sqrt{42} + 18} right )}$$

$$frac{sqrt{42}}{84} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$

0.077151674981046*log((12*x – 2*sqrt(42))/(2*sqrt(42) + 12*x))

$$frac{sqrt{42}}{84} log{left (frac{6 x^{2} – 2 sqrt{42} x + 7}{6 x^{2} – 7} right )}$$

$$frac{sqrt{42}}{84} log{left (frac{6 x – sqrt{42}}{6 x + sqrt{42}} right )}$$

/ ____
____ |- / 42 + 6*x|
/ 42 *log|————–|
| ____ |
/ 42 + 6*x /
————————–
84

$$frac{sqrt{42}}{84} log{left (frac{6 x – sqrt{42}}{6 x + sqrt{42}} right )}$$

$$frac{sqrt{42}}{84} log{left (frac{6 x – sqrt{42}}{6 x + sqrt{42}} right )}$$

/ ____
____ |12*x – 2*/ 42 |
/ 42 *log|—————|
| ____ |
2*/ 42 + 12*x/
—————————
84

$$frac{sqrt{42}}{84} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$

/ ____
____ | / 42 6*x |
/ 42 *log|- ———— + ————|
| ____ ____ |
/ 42 + 6*x / 42 + 6*x/
—————————————–
84

$$frac{sqrt{42}}{84} log{left (frac{6 x}{6 x + sqrt{42}} – frac{sqrt{42}}{6 x + sqrt{42}} right )}$$

/ ____
____ | 2*/ 42 12*x |
/ 42 *log|- ————— + —————|
| ____ ____ |
2*/ 42 + 12*x 2*/ 42 + 12*x/
———————————————–
84

$$frac{sqrt{42}}{84} log{left (frac{12 x}{12 x + 2 sqrt{42}} – frac{2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$

____ / / ____ / ____
/ 42 * – log2*/ 42 + 12*x/ + log – 2*/ 42 + 12*x//
——————————————————–
84

$$frac{sqrt{42}}{84} left(log{left (12 x – 2 sqrt{42} right )} – log{left (12 x + 2 sqrt{42} right )}right)$$

/ ____
____ |12*x – 2*/ 42 |
/ 42 *log|—————|
| ____ |
2*/ 42 + 12*x/
—————————
84

$$frac{sqrt{42}}{84} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$