$$\frac{2}{t+10}-\frac{1}{t+1}=\frac{1}{t+2}$$
$t = -\frac{26}{17} = -1\frac{9}{17} \approx -1.529411765$
$$\left(t+1\right)\left(t+2\right)\times 2-\left(t+2\right)\left(t+10\right)=\left(t+1\right)\left(t+10\right)$$
$$\left(t^{2}+3t+2\right)\times 2-\left(t+2\right)\left(t+10\right)=\left(t+1\right)\left(t+10\right)$$
$$2t^{2}+6t+4-\left(t+2\right)\left(t+10\right)=\left(t+1\right)\left(t+10\right)$$
$$2t^{2}+6t+4-\left(t^{2}+12t+20\right)=\left(t+1\right)\left(t+10\right)$$
$$2t^{2}+6t+4-t^{2}-12t-20=\left(t+1\right)\left(t+10\right)$$
$$t^{2}+6t+4-12t-20=\left(t+1\right)\left(t+10\right)$$
$$t^{2}-6t+4-20=\left(t+1\right)\left(t+10\right)$$
$$t^{2}-6t-16=\left(t+1\right)\left(t+10\right)$$
$$t^{2}-6t-16=t^{2}+11t+10$$
$$t^{2}-6t-16-t^{2}=11t+10$$
$$-6t-16=11t+10$$
$$-6t-16-11t=10$$
$$-17t-16=10$$
$$-17t=10+16$$
$$-17t=26$$
$$t=\frac{26}{-17}$$
$$t=-\frac{26}{17}$$
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