b $$ \frac{3 a}{2}+\frac{b}{4}-\frac{5 b}{3}-\frac{5 a}{8} $$

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Calculate or simplify the expression $$ \frac{3a}{2}+\frac{b}{4}-\frac{5b}{3}-\frac{5a}{8} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{3a}{2}+\frac{b}{4}-\frac{5b}{3}-\frac{5a}{8}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{3a	imes 2	imes 2	imes 3}{2	imes 2	imes 2	imes 3}+\frac{b	imes 2	imes 3}{4	imes 2	imes 3}-\frac{5b	imes 2	imes 2	imes 2}{3	imes 2	imes 2	imes 2}-\frac{5a	imes 3}{8	imes 3}$$
- step2: Multiply the terms:
  $$\frac{3a	imes 2	imes 2	imes 3}{24}+\frac{b	imes 2	imes 3}{4	imes 2	imes 3}-\frac{5b	imes 2	imes 2	imes 2}{3	imes 2	imes 2	imes 2}-\frac{5a	imes 3}{8	imes 3}$$
- step3: Multiply the terms:
  $$\frac{3a	imes 2	imes 2	imes 3}{24}+\frac{b	imes 2	imes 3}{24}-\frac{5b	imes 2	imes 2	imes 2}{3	imes 2	imes 2	imes 2}-\frac{5a	imes 3}{8	imes 3}$$
- step4: Multiply the terms:
  $$\frac{3a	imes 2	imes 2	imes 3}{24}+\frac{b	imes 2	imes 3}{24}-\frac{5b	imes 2	imes 2	imes 2}{24}-\frac{5a	imes 3}{8	imes 3}$$
- step5: Multiply the numbers:
  $$\frac{3a	imes 2	imes 2	imes 3}{24}+\frac{b	imes 2	imes 3}{24}-\frac{5b	imes 2	imes 2	imes 2}{24}-\frac{5a	imes 3}{24}$$
- step6: Transform the expression:
  $$\frac{3a	imes 2	imes 2	imes 3+b	imes 2	imes 3-5b	imes 2	imes 2	imes 2-5a	imes 3}{24}$$
- step7: Multiply the terms:
  $$\frac{36a+b	imes 2	imes 3-5b	imes 2	imes 2	imes 2-5a	imes 3}{24}$$
- step8: Multiply the terms:
  $$\frac{36a+6b-5b	imes 2	imes 2	imes 2-5a	imes 3}{24}$$
- step9: Multiply the terms:
  $$\frac{36a+6b-40b-5a	imes 3}{24}$$
- step10: Multiply the terms:
  $$\frac{36a+6b-40b-15a}{24}$$
- step11: Calculate:
  $$\frac{21a-34b}{24}$$
The simplified form of the expression $$ \frac{3a}{2}+\frac{b}{4}-\frac{5b}{3}-\frac{5a}{8} $$ is $$ \frac{21a-34b}{24} $$.
$$ \frac{21a-34b}{24} $$

b \( \frac{3 a}{2}+\frac{b}{4}-\frac{5 b}{3}-\frac{5 a}{8} \)

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