Solve c = binomial(8,5) - 7/3 * binomial(44,45) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$c=\binom{8}{5}-\frac{7}{3}\times\binom{44}{45}$$

Solve for c

$c=-\frac{92}{135}\approx -0.681481481$

Steps for Solving Linear Equation

Multiply $\frac{7}{3}$ times $\frac{44}{45}$ by multiplying numerator times numerator and denominator times denominator.

$$c=\frac{8}{5}-\frac{7\times 44}{3\times 45}$$

Do the multiplications in the fraction $\frac{7\times 44}{3\times 45}$.

$$c=\frac{8}{5}-\frac{308}{135}$$

Least common multiple of $5$ and $135$ is $135$. Convert $\frac{8}{5}$ and $\frac{308}{135}$ to fractions with denominator $135$.

$$c=\frac{216}{135}-\frac{308}{135}$$

Since $\frac{216}{135}$ and $\frac{308}{135}$ have the same denominator, subtract them by subtracting their numerators.

$$c=\frac{216-308}{135}$$

Subtract $308$ from $216$ to get $-92$.

$$c=-\frac{92}{135}$$

Assign c

$c≔-\frac{92}{135}$