"without care" is correct and can be used in written English.
Example sentence: She signed the contract without care, not knowing what she was really agreeing to.
The result is that thousands go without care every year.
As Bales puts it: "employers who can destroy the environment without care are often the ones who can destroy lives without care".
Too often it is made industrially, as if it were slapped together without care or precision.
He used the most expensive ingredients but assembled the food without care, without harmony of flavors.
The one exception was low-income people in poor health, who went without care they needed.
"Since last night the patients [have been] left without care and food," said Maiga.
And we're scared sometimes, but not scared enough to leave women without choices and without care.
As the women succumb to AIDS, the children are left without care or supervision.
"Others have fled in fear, leaving people without care for even the most common illnesses.
Critics rightly accused the US of employing neo-Hessians in Iraq without care for the consequences.
How splendid to bathe in a Surrey lake so gladly and without care!
