Solve 76-h/t+213=77-h/T+273

$$\frac { 76 - h } { t + 213 } = \frac { 77 - h } { T + 273 }$$

Solve for T

$$T=-\frac{ht-77t-60h+4347}{76-h}$$

$$t\neq -213\text{ and }h\neq 77\text{ and }h\neq 76$$

Steps for Solving Linear Equation

Variable T cannot be equal to -273 since division by zero is not defined. Multiply both sides of the equation by \left(T+273\right)\left(t+213\right), the least common multiple of t+213,T+273.

$$\left(T+273\right)\left(76-h\right)=\left(t+213\right)\left(77-h\right)$$

Use the distributive property to multiply T+273 by 76-h.

$$76T-Th+20748-273h=\left(t+213\right)\left(77-h\right)$$

Use the distributive property to multiply t+213 by 77-h.

$$76T-Th+20748-273h=77t-th+16401-213h$$

Subtract 20748 from both sides.

$$76T-Th-273h=77t-th+16401-213h-20748$$

Subtract 20748 from 16401 to get -4347.

$$76T-Th-273h=77t-th-4347-213h$$

Add 273h to both sides.

$$76T-Th=77t-th-4347-213h+273h$$

Combine -213h and 273h to get 60h.

$$76T-Th=77t-th-4347+60h$$

Combine all terms containing T.

$$\left(76-h\right)T=77t-th-4347+60h$$

The equation is in standard form.

$$\left(76-h\right)T=-ht+77t+60h-4347$$

Divide both sides by 76-h.

$$\frac{\left(76-h\right)T}{76-h}=\frac{-ht+77t+60h-4347}{76-h}$$

Dividing by 76-h undoes the multiplication by 76-h.

$$T=\frac{-ht+77t+60h-4347}{76-h}$$

Variable T cannot be equal to -273.

$$T=\frac{-ht+77t+60h-4347}{76-h}\text{, }T\neq -273$$

Solve for h

$$h=-\frac{4347+76T-77t}{t-T-60}$$

$$t\neq T+60\text{ and }t\neq -213\text{ and }T\neq -273$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(T+273\right)\left(t+213\right), the least common multiple of t+213,T+273.

$$\left(T+273\right)\left(76-h\right)=\left(t+213\right)\left(77-h\right)$$

Use the distributive property to multiply T+273 by 76-h.

$$76T-Th+20748-273h=\left(t+213\right)\left(77-h\right)$$

Use the distributive property to multiply t+213 by 77-h.

$$76T-Th+20748-273h=77t-th+16401-213h$$

Add th to both sides.

$$76T-Th+20748-273h+th=77t+16401-213h$$

Add 213h to both sides.

$$76T-Th+20748-273h+th+213h=77t+16401$$

Combine -273h and 213h to get -60h.

$$76T-Th+20748-60h+th=77t+16401$$

Subtract 76T from both sides.

$$-Th+20748-60h+th=77t+16401-76T$$

Subtract 20748 from both sides.

$$-Th-60h+th=77t+16401-76T-20748$$

Subtract 20748 from 16401 to get -4347.

$$-Th-60h+th=77t-4347-76T$$

Combine all terms containing h.

$$\left(-T-60+t\right)h=77t-4347-76T$$

The equation is in standard form.

$$\left(t-T-60\right)h=77t-76T-4347$$

Divide both sides by t-T-60.

$$\frac{\left(t-T-60\right)h}{t-T-60}=\frac{77t-76T-4347}{t-T-60}$$

Dividing by t-T-60 undoes the multiplication by t-T-60.

$$h=\frac{77t-76T-4347}{t-T-60}$$