Simplify (a) (t-4)/(5t)÷(16-t^(2))/(10t^(2)s),

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Simplify (a)  (t-4)/(5t)÷(16-t^(2))/(10t^(2)s),

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Write Expression and Identify Operation: Write down the given expression and identify the operation to be performed. We are given the expression (t-4)/(5t) ÷ (16-t^2)/(10t^2s). We need to divide the first fraction by the second fraction.Convert Division into Multiplication: Convert the division of fractions into multiplication by the reciprocal of the second fraction. The expression (t-4)/(5t) ÷ (16-t^2)/(10t^2s) can be rewritten as (t-4)/(5t) * (10t^2s)/(16-t^2).Factor Denominator of Second Fraction: Factor the denominator of the second fraction if possible. The term 16-t^2 is a difference of squares and can be factored as (4+t)(4-t). So, the expression becomes (t-4)/(5t) * (10t^2s)/((4+t)(4-t)).Simplify by Canceling Common Factors: Simplify the expression by canceling out common factors. We notice that (t-4) and (4-t) are the same terms with opposite signs, so they cancel each other out as -1. We also cancel out t from the numerator of the first fraction and the denominator of the second fraction. The expression simplifies to -1/(5) * (10s)/(4+t).Multiply Numerators and Denominators: Multiply the numerators and denominators of the remaining fractions. Multiplying the numerators: -1 * 10s = -10s Multiplying the denominators: 5 * (4+t) = 20 + 5t The simplified expression is -10s/(20 + 5t).Check for Further Simplification: Check for any further simplification. The expression -10s/(20 + 5t) cannot be simplified further as there are no common factors to cancel out.

Simplify $\newline$ (a) $\frac{t-4}{5 t} \div \frac{16-t^{2}}{10 t^{2} s}$ ,

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Simplify\newline(a) t−45t÷16−t210t2s \frac{t-4}{5 t} \div \frac{16-t^{2}}{10 t^{2} s} 5tt−4​÷10t2s16−t2​,

Simplify $\newline$ (a) $\frac{t-4}{5 t} \div \frac{16-t^{2}}{10 t^{2} s}$ ,